Add files using upload-large-folder tool

-NE4T4oBgHgl3EQf3w1M/content/2301.05308v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cb15380bf1e3a1f8b4416919b9927e7bcb47ccc4dcb9bffe0be81d0de553810b
+size 779413

-NE4T4oBgHgl3EQf3w1M/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f4cf06bc7a7b29a8407541611429447a83bf44cc1a24c9b6a02750faf8545093
+size 5046317

-NE4T4oBgHgl3EQf3w1M/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c1b0b8b531133787518bb2e2a7ab8a9d041ae4994a35c9e1de01834d921c76ce
+size 198552

-dE1T4oBgHgl3EQfUgPr/content/2301.03092v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:963ff41fd0c03920ac247feda7e3de266016de0759e6387e397ed24092f0a1c1
+size 2498776

-dE1T4oBgHgl3EQfUgPr/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7025cfd42d584d682d8af5cc1bc49556918e3d3157010e9a7c7a21eaa300214e
+size 3473453

.gitattributes

@@ -8591,3 +8591,71 @@ HdE1T4oBgHgl3EQfXgSr/content/2301.03128v1.pdf filter=lfs diff=lfs merge=lfs -tex
 adFPT4oBgHgl3EQfvjWp/content/2301.13160v1.pdf filter=lfs diff=lfs merge=lfs -text
 UdE0T4oBgHgl3EQf2gJy/content/2301.02713v1.pdf filter=lfs diff=lfs merge=lfs -text
 T9AyT4oBgHgl3EQf8fpt/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+CtFJT4oBgHgl3EQfAiym/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+HdE1T4oBgHgl3EQfXgSr/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+2dFAT4oBgHgl3EQfDhxB/content/2301.08416v1.pdf filter=lfs diff=lfs merge=lfs -text
+ZtAzT4oBgHgl3EQfK_te/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+adFPT4oBgHgl3EQfvjWp/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+CtFJT4oBgHgl3EQfAiym/content/2301.11421v1.pdf filter=lfs diff=lfs merge=lfs -text
+CNE3T4oBgHgl3EQfUQpw/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+PtAzT4oBgHgl3EQfWvyr/content/2301.01307v1.pdf filter=lfs diff=lfs merge=lfs -text
+2dFAT4oBgHgl3EQfDhxB/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+m9AzT4oBgHgl3EQfqP2M/content/2301.01626v1.pdf filter=lfs diff=lfs merge=lfs -text
+PNE0T4oBgHgl3EQf1AIP/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+hdAyT4oBgHgl3EQfkPgm/content/2301.00428v1.pdf filter=lfs diff=lfs merge=lfs -text
+39AyT4oBgHgl3EQfo_il/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+wtFPT4oBgHgl3EQfPjQO/content/2301.13038v1.pdf filter=lfs diff=lfs merge=lfs -text
+9dE4T4oBgHgl3EQfDQsU/content/2301.04867v1.pdf filter=lfs diff=lfs merge=lfs -text
+-NE4T4oBgHgl3EQf3w1M/content/2301.05308v1.pdf filter=lfs diff=lfs merge=lfs -text
+f9A0T4oBgHgl3EQfHv-A/content/2301.02065v1.pdf filter=lfs diff=lfs merge=lfs -text
+lNE2T4oBgHgl3EQfIwaA/content/2301.03684v1.pdf filter=lfs diff=lfs merge=lfs -text
+y9FLT4oBgHgl3EQfnS-e/content/2301.12127v1.pdf filter=lfs diff=lfs merge=lfs -text
+v9E4T4oBgHgl3EQfXQwv/content/2301.05039v1.pdf filter=lfs diff=lfs merge=lfs -text
+4dFIT4oBgHgl3EQf6yuB/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+-dE1T4oBgHgl3EQfUgPr/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+WNFRT4oBgHgl3EQf9DhY/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+0dAyT4oBgHgl3EQfbfdc/content/2301.00263v1.pdf filter=lfs diff=lfs merge=lfs -text
+6tAzT4oBgHgl3EQfgPwz/content/2301.01464v1.pdf filter=lfs diff=lfs merge=lfs -text
+wtFPT4oBgHgl3EQfPjQO/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+R9E0T4oBgHgl3EQfUgAs/content/2301.02250v1.pdf filter=lfs diff=lfs merge=lfs -text
+p9AzT4oBgHgl3EQfOvtl/content/2301.01171v1.pdf filter=lfs diff=lfs merge=lfs -text
+rNFQT4oBgHgl3EQftzab/content/2301.13393v1.pdf filter=lfs diff=lfs merge=lfs -text
+b9AzT4oBgHgl3EQf2_6M/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+PtAzT4oBgHgl3EQfWvyr/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+hdE5T4oBgHgl3EQfFQ6l/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+0dAyT4oBgHgl3EQfbfdc/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+K9FAT4oBgHgl3EQfwR5T/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+ZtAzT4oBgHgl3EQfK_te/content/2301.01106v1.pdf filter=lfs diff=lfs merge=lfs -text
+K9AzT4oBgHgl3EQfkP22/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+NdFOT4oBgHgl3EQf2jRR/content/2301.12942v1.pdf filter=lfs diff=lfs merge=lfs -text
+fdA0T4oBgHgl3EQfHf_u/content/2301.02063v1.pdf filter=lfs diff=lfs merge=lfs -text
+2tAzT4oBgHgl3EQffPw3/content/2301.01448v1.pdf filter=lfs diff=lfs merge=lfs -text
+K9FAT4oBgHgl3EQfwR5T/content/2301.08680v1.pdf filter=lfs diff=lfs merge=lfs -text
+1dAzT4oBgHgl3EQfRfuL/content/2301.01217v1.pdf filter=lfs diff=lfs merge=lfs -text
+ndAyT4oBgHgl3EQf__rr/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+fdA0T4oBgHgl3EQfHf_u/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+V9AzT4oBgHgl3EQfmP0G/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+1dAzT4oBgHgl3EQfRfuL/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+rNFQT4oBgHgl3EQftzab/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+AtE2T4oBgHgl3EQfRQeF/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+-dE1T4oBgHgl3EQfUgPr/content/2301.03092v1.pdf filter=lfs diff=lfs merge=lfs -text
+b9AzT4oBgHgl3EQf2_6M/content/2301.01823v1.pdf filter=lfs diff=lfs merge=lfs -text
+AtE2T4oBgHgl3EQfRQeF/content/2301.03779v1.pdf filter=lfs diff=lfs merge=lfs -text
+MdE1T4oBgHgl3EQfZQR8/content/2301.03148v1.pdf filter=lfs diff=lfs merge=lfs -text
+V9AzT4oBgHgl3EQfmP0G/content/2301.01558v1.pdf filter=lfs diff=lfs merge=lfs -text
+BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf filter=lfs diff=lfs merge=lfs -text
+nNAzT4oBgHgl3EQfN_vv/content/2301.01160v1.pdf filter=lfs diff=lfs merge=lfs -text
+a9E4T4oBgHgl3EQfPAy5/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+-NE4T4oBgHgl3EQf3w1M/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+WdFIT4oBgHgl3EQfhytq/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+tNE1T4oBgHgl3EQfjgS9/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+p9AzT4oBgHgl3EQfOvtl/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+StE0T4oBgHgl3EQfUwAJ/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+mtFLT4oBgHgl3EQffC-V/content/2301.12093v1.pdf filter=lfs diff=lfs merge=lfs -text
+29E1T4oBgHgl3EQf5wUG/content/2301.03514v1.pdf filter=lfs diff=lfs merge=lfs -text
+BNE1T4oBgHgl3EQfpQVQ/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf filter=lfs diff=lfs merge=lfs -text
+m9AzT4oBgHgl3EQfqP2M/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+CNE3T4oBgHgl3EQfUQpw/content/2301.04449v1.pdf filter=lfs diff=lfs merge=lfs -text
+QNFJT4oBgHgl3EQfJSzf/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+a9AyT4oBgHgl3EQfiviR/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text

0dAyT4oBgHgl3EQfbfdc/content/2301.00263v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:383d104b63d3c704f0d7a1730b5560ad914a6d87b986501fedfa9d25fa348190
+size 212710

0dAyT4oBgHgl3EQfbfdc/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:886c731c1cd7d302dcf5a5f6f276cbb90134c04516ea93377d8cf5bd5af30fb5
+size 2818093

0dAyT4oBgHgl3EQfbfdc/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e3c8a04fe5dd497b18de5fba25ecb2361cfcb4708379b4f3c58ed77913246e4c
+size 106120

19FAT4oBgHgl3EQfkR2N/content/tmp_files/2301.08610v1.pdf.txt

@@ -0,0 +1,1284 @@
+Platform for Probing Radiation Transport Properties of Hydrogen at Conditions
+Found in the Deep Interiors of Red Dwarfs
+J. Lütgert,1, 2, 3, ∗ M. Bethkenhagen,4 B. Bachmann,5 L. Divol,5 D. O. Gericke,6 S. H. Glenzer,7
+G. N. Hall,5 N. Izumi,5 S. F. Khan,5 O. L. Landen,5 S. A. MacLaren,5 L. Masse,5, 8
+R. Redmer,1 M. Schörner,1 M. O. Schölmerich,5 S. Schumacher,1 N. R. Shaffer,9
+C. E. Starrett,10 P. A. Sterne,5 C. Trosseille,5 T. Döppner,5 and D. Kraus1, 2, †
+1Institut für Physik, Universität Rostock, Albert-Einstein-Str. 23, 18059 Rostock, Germany
+2Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstrasse 400, 01328 Dresden, Germany
+3Institute of Nuclear and Particle Physics, Technische Universität Dresden, 01069 Dresden, Germany
+4École Normale Supérieure de Lyon, Université Lyon 1,
+Laboratoire de Géologie de Lyon, CNRS UMR 5276, 69364 Lyon Cedex 07, France
+5Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
+6Centre for Fusion, Space and Astrophysics, Department of Physics,
+University of Warwick, Coventry CV4 7AL, United Kingdom
+7SLAC National Accelerator Laboratory, Menlo Park, CA 94309, USA
+8CEA-DAM, DIF, F-91297 Arpajon, France
+9Laboratory for Laser Energetics, University of Rochester,
+250 East River Road, Rochester, NY 14623, USA
+10Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM 87545, USA
+(Dated: January 23, 2023)
+We describe an experimental concept at the National Ignition Facility for specifically tailored
+spherical implosions to compress hydrogen to extreme densities (up to ∼ 800× solid density,
+electron number density ne ∼ 4 × 1025 cm−3) at moderate temperatures (T ∼ 200 eV), i.e., to
+conditions, which are relevant to the interiors of red dwarf stars. The dense plasma will be probed
+by laser-generated x-ray radiation of different photon energy to determine the plasma opacity due
+to collisional (free-free) absorption and Thomson scattering. The obtained results will benchmark
+radiation transport models, which in the case for free-free absorption show strong deviations at
+conditions relevant to red dwarfs. This very first experimental test of free-free opacity models at
+these extreme states will help to constrain where inside those celestial objects energy transport is
+dominated by radiation or convection. Moreover, our study will inform models for other important
+processes in dense plasmas, which are based on electron-ion collisions, e.g., stopping of swift ions or
+electron-ion temperature relaxation.
+I.
+INTRODUCTION
+Red dwarfs (M dwarfs) are the lightest and coolest
+main sequence stars and make up ∼ 70 % of all stars
+in the Sun’s neighborhood. [1, 2] Prominent examples
+are our nearest neighbor Proxima Centauri (0.12 M⊙)
+or TRAPPIST-1 (0.089 M⊙),
+which is only slightly
+larger than Jupiter, but much more massive.
+The
+interiors of red dwarfs mainly consist of hydrogen-
+helium mixtures, which are progressively shaped by
+screening effects, ion-ion correlations, and degeneracy
+as temperature decreases and density increases. [3]
+These many-particle effects are challenging to model, in
+particular, for calculations of radiation transport, which
+plays a major role in modeling of sub-stellar objects and
+stars. From the solar abundance problem, we know that
+∼ 20 % changes in opacity have paramount impact on
+our understanding of stellar interiors. [4, 5] Whether
+energy can effectively be transported via radiation or,
+if radiation is not sufficient, convection sets in, is a
+∗ [email protected]
+† [email protected]
+property that is particularly influenced by stellar opacity.
+In general, the physics of red dwarfs is poorly understood
+in comparison with the hotter interior of the Sun, which
+is much closer to the ideal plasma state.
+Figure 1 shows simulated pressure-temperature profiles
+of stars on the main sequence, demonstrating the extreme
+plasma conditions present inside those celestial objects.
+The curves were obtained using the MESA code for
+stellar evolution [6–10] (see the appendix for details on
+these simulations).
+The inset illustrates the schematic
+interiors of stars from the core (m/M = 0) to the
+photosphere (m/M = 1) divided into radiative and
+convective zones for stars with a solar composition of
+elements.
+Red dwarfs are characterized by masses
+between 0.075 and 0.5 solar masses so that their typical
+mass-temperature ratios overall place red dwarfs in a
+regime, where convection dominates the outer regions.
+Depending on the size of the individual object, a more or
+less developed radiative core is present.
+The smallest
+red dwarfs (M
+≲
+0.2 M⊙) are thought to be fully
+convective.
+In this case, the fusion reactions in the
+core are permanently re-fueled by hydrogen from the
+outer layers. Combined with the low fusion rates due to
+the relatively low core temperatures, convection possibly
+arXiv:2301.08610v1  [physics.plasm-ph]  20 Jan 2023
+
+2
+FIG. 1.
+Pressure-temperature profiles for various celestial
+objects calculated using the MESA package. [6–10] Solid
+lines denote convective regions while dots indicate a layer of
+radiative energy transport. The gray shaded area shows the
+conditions, which we intent to generate in our experiment.
+Inset: Mass coordinate m/M along stellar interior profiles for
+objects with solar composition divided into radiative (white,
+dotted lines) and convective (gray, solid curves) regions over
+total object mass M relative to the Sun’s mass M⊙. The gray-
+scale dataset was published by Kippenhahn et al. [11] while
+the colored lines show the MESA calculations of the main
+figure.
+allows some red dwarfs to last trillions of years until
+all hydrogen fuel is exhausted. However, even a small
+radiative core can strongly change this behavior and
+its existence crucially depends on the effectiveness of
+radiation transport in highly compressed matter.
+Moreover, the internal structure of a star has a
+major impact on the activity of its surface. [12] The
+boundary between a radiative core and a convective
+layer can lead to strong magnetic fields and a turbulent
+atmosphere, [1, 13, 14] including radiative and plasma
+outbursts that may threaten life on nearby planets.
+Therefore, understanding the radiative properties of the
+complex plasmas within a host star is crucial when
+judging the possibility of an exoplanet to host life –
+especially for red dwarfs where the habitable zone is
+thought to be found relatively close to the star itself due
+to the low surface temperature. [15]
+For red dwarf stars, the thermodynamic conditions
+at the boundary between radiative core and convective
+envelope are estimated to be in a pressure regime of few
+Gbars and temperatures of few million Kelvin. [1, 11]
+Corresponding free electron densities are in the range of
+few 1025 cm−3, which results in Fermi energies of similar
+order as the thermal energy of the free electrons. The
+energy transport in this so-called warm dense matter
+regime [16] is extremely difficult to calculate, which gives
+rise to significant uncertainties in modeling the energy
+transport inside red dwarfs.
+II.
+THEORY
+For stellar interiors, the radiative opacity κrad is
+usually divided into three contributions: [17]
+κrad = κbf + κff + κT ,
+(1)
+where κbf is the opacity contribution by bound-free
+absorption, κff denotes the free-free contribution and
+κT = ZσT /mi the absorption due to Thomson scattering
+from free electrons, which is solely dependent on the
+Thomson scattering transport cross section σT , [18, 19]
+the average ion charge state Z and the average ion mass
+mi of the plasma. While Rayleigh scattering might be of
+interest for the atmosphere of K and M class stars, [20]
+the high ionization in hotter photospheres and deep
+within even the smallest stars often justifies to neglect its
+contribution to κrad. For the solar abundance problem,
+the bound-free opacity of metals is probably most
+relevant, but deep in the solar radiation zone as well as for
+many red dwarfs, particularly those with low metallicity,
+hydrogen free-free opacity, i.e., absorption due to inverse
+bremsstrahlung, is the dominant absorption mechanism
+of radiation. [17] For these red dwarfs, the absolute values
+for free-free absorption determine where convection
+or radiation will be the dominant energy transport
+mechanism.
+Figure 2 shows a density-temperature diagram of
+dominating
+absorption
+mechanisms
+thought
+to
+be
+present for the composition of population I stars in
+comparison with red dwarf interiors and the Sun. While
+bound-free transitions dominate at low densities and
+temperatures, free-free absorption starts to outrun the
+bound-free opacity with the increase in density due to
+increasing electron-ion collision rates as well as pressure
+ionization of heavier elements. [21] At the highest
+densities, conduction by degenerate electrons becomes
+more efficient than radiation transport, whereas for low
+densities and highest temperatures, photon scattering
+from electrons (Thomson or Compton, depending on
+photon energy) is most significant.
+A.
+Analytical models
+A classical
+treatment of
+the spectral absorption
+coefficient due to inverse bremsstrahlung, derived from
+the description of electron-ion collisions in a weakly
+coupled plasma environment, yields for the absorption
+coefficient αff, [22]
+αff(ν) = ρκff(ν) ∝ Z2neni
+ν3√
+T
+�
+1 − exp
+�
+− hν
+kBT
+��
+gff(ν, T),
+(2)
+
+.3
+FIG. 2.
+Dominating opacities in different regimes of the
+density-temperature diagram for a composition of elements as
+in population I stars. [17] The colored lines show densities and
+temperatures realized within main-sequence stars according
+to the “MESA” stellar evolution code [6–10] with solid lines
+representing convective layers. The proposed experiments will
+probe conditions similar to the interiors of red dwarf stars
+where free-free absorption is expected to dominate (indicated
+by the shaded region).
+where ν denotes the x-ray frequency, ρ is the mass
+density, Z is the average degree of ionization, ne is
+the free electron number density, ni is the ion number
+density, T is the plasma temperature, h is Planck’s
+constant, and kB is Boltzmann’s constant.
+Additional
+corrections due to quantum and correlation effects are
+accounted for in a frequency-dependent correction factor
+gff(ν, T), the so-called Gaunt factor. [23] For a weakly
+coupled ideal plasma, the Gaunt factor can be interpreted
+as the logarithm of the ratio of maximum impact
+parameter bmax and minimum impact parameter bmin
+in the corresponding electron-ion collision (the so-called
+Coulomb logarithm [24]):
+gff(ν, T) =
+√
+3
+π ln
+�bmax
+bmin
+�
+.
+(3)
+This formalism is equivalent to the classical treatment
+of several other important plasma effects that involve
+Coulomb collisions of electrons and ions, e.g., stopping
+power of ions or electron-ion temperature equilibration
+in dense plasmas. [25] The maximum impact parameter
+bmax is usually given by min(ve/2πν, λs) where ve is the
+average velocity of the electrons, ν is the x-ray frequency,
+and λs is the screening length due to the surrounding
+plasma. On the other hand, bmin can be expressed as
+max(b⊥, λth), where b⊥ = Ze2/(4πϵ0mev2
+e) is the impact
+parameter for an electron being deflected perpendicular
+to its direction of incidence and λth denotes the thermal
+de Broglie wavelength of the electrons.
+However, for conditions relevant to the interiors of
+red dwarfs [e.g., ne ∼ few 1025 cm−3, Te ∼ few 100 eV
+(Ref. [3])], we find ve/2πν
+<
+λth, i.e., a negative
+Coulomb logarithm for x-ray frequencies larger than the
+plasma frequency. Thus, this simple classical treatment
+assuming a weakly coupled plasma is not appropriate
+for
+such
+conditions.
+Indeed,
+more
+sophisticated
+approaches have been developed to accommodate these
+conditions. [26, 27]
+B.
+Average Atom and Density Functional Theory
+calculations
+Figure 3 shows Average Atom calculations with a
+Mean Force potential (AA-MF) [28] and state-of-the-
+art Density Functional Theory Molecular Dynamics
+(DFT-MD) simulations [29] compared to the analytical
+model for the free-free opacity with constant Gaunt
+factor and calculations by van Hoof et al. [30, 31]
+The
+first
+two
+simulation
+methods
+have
+previously
+been applied successfully for calculating the equation-
+of-state
+(EOS)
+and
+transport
+properties
+of
+dense
+plasmas. [28, 32–34] The DFT-MD simulations were
+performed
+with
+up
+to
+256
+hydrogen
+atoms
+using
+the program package VASP. [35–38] Our considered
+density range spans 20 −150 g cm−3 at 100, 150, and
+200 eV. The simulations use the Baldereschi mean value
+point [39] and the Coulomb potential with an energy
+cutoff of 10 000 eV.
+Each DFT-MD point was run for
+20 000 time steps with a time step size between 3 as
+(attoseconds) and 8 as depending on the thermodynamic
+conditions.
+The temperature was controlled with
+a Nosé-Hoover thermostat. [40] Subsequently,
+10 –
+20 snapshots were selected from each trajectory to
+calculate the electrical conductivity and opacity applying
+the
+Kubo-Greenwood
+formalism
+[41,
+42]
+and
+the
+Kramers-Kronig relation.
+For details on the AA-
+MF calculations (which were performed for identical
+temperatures
+and
+pressures),
+we
+refer
+to
+previous
+publications. [28, 43–46]
+While the DFT-MD simulation naturally includes
+many-body effects in the description of wavefunctions
+and the density of states due to the multiple ions included
+in the simulation, the AA-MF approach, which is strictly
+speaking also DFT-based, simplifies the calculation by
+exclusively relying on the atom-in-jellium model. Either
+of the two formulations calculates opacity from the real
+part of the electrical conductivity.
+Both approaches
+agree on the quantity of extinction remarkably well,
+supporting each other.
+This result is particularly
+noteworthy as the similarity of the AA-MF calculation
+with DFT-MD – for the specific case of hydrogen –
+is highly desired:
+While DFT-MD is generally more
+accurate, AA-MF is computationally significantly less
+expensive and should be favored if benchmarks can
+show good agreement between the two methods.
+At
+the same time, the consistency of the computed opacity
+illustrates impressively that extreme states of matter
+can be treated by DFT-MD nowadays with the increase
+
+:4
+FIG. 3. Opacity for a (25 %/75 %) HT mixture at an electron
+density ne = 5 × 1025 cm−3 and a temperature of T
+=
+100 eV (solid and dotted lines) or T
+= 150 eV (dashed),
+respectively, according to different models.
+The blue and
+purple lines depict DFT-MD and AA-MF calculations. The
+other solid curves show the analytical model for free-free
+extinction [Eq. (2)] with a Gaunt factor equal to unity
+(black line) or values calculated by van Hoof et al. [30, 31]
+(red). For comparison, the opacity due to Thomson scattering
+for a temperature of T = 100 eV is shown as the dotted
+black line.
+The AA-MF calculation at 150 eV and the
+inset depicting the relative difference between the two results
+[∆κAA = 2(κ150 eV
+AA
+− κ100 eV
+AA
+)/(κ150 eV
+AA
++ κ100 eV
+AA
+)] show that
+the temperature influence is very small for photon energies
+above 3 keV due to the degenerate conditions.
+in computational power and, hence, number of energy
+bands included in the calculation.
+Both methods show a discrepancy to the calculation
+of the free-free opacity from the semi-classical formula
+[Eq. (2)], as it can be seen in Fig. 3.
+The simplest
+approach of setting the Gaunt factor to unity reproduces
+the classical result of Kramers. [22] Introducing quantum-
+mechanical corrections, van Hoof et al. [30, 31] provide
+easily applicable, tabulated values for gff by following
+the seminal work of Karzas and Latter. [47] However, this
+calculation is requiring more assumptions than the AA-
+MF or the DFT-MD model, e.g., the velocity distribution
+of the electrons (with is assumed to be Maxwellian) in
+order to calculate thermally averaged free-free Gaunt
+factors and from these opacities. [30, 31] Other authors
+perform similar calculations but integrate over the Fermi
+distribution of a degenerate electron gas. [24]
+In fact, for dense plasma conditions comparable to
+the interiors of main sequence stars, even advanced
+calculations of the Gaunt factor vary by more than 50 %
+for frequencies larger than the plasma frequency. [27] In
+particular, the specific treatment of dynamic screening,
+strong collisions, and re-normalization due to higher
+moments can make a significant difference in comparison
+to widely-used Born approximation treatments of the
+Gaunt factor. [27] Deviations are particularly significant
+in the photon energy regime from ∼ 500 eV to few keV,
+which is the dominant contribution when calculating the
+Rosseland mean opacity for the Sun and smaller stars.
+Indeed, varying the opacity by 50 % can change the radii
+of the boundaries between convection and radiation zone
+by up to 10 %, which, given the underlying density and
+temperature gradients, would significantly impact our
+general understanding of stars. [5, 48]
+III.
+EXPERIMENTAL CONCEPT
+Using the largest laser system in the world, namely, the
+National Ignition Facility (NIF) at Lawrence Livermore
+National Laboratory, [49] it is now possible to create
+and probe matter states relevant to stellar interiors in
+the laboratory. [50, 51] To address the questions raised
+above, we have developed a concept to leverage NIF’s
+unique capabilities to create relevant conditions and
+obtain a very first test of free-free opacity models in
+this very important plasma regime via x-ray absorption
+measurements of highly compressed hydrogen during
+the stagnation phase of layered capsule implosions. In
+this way, not only the various existing models and
+resulting tables for the Gaunt factor will be tested, but
+also modern DFT-MD and AA-MF simulations, which
+provide the absorption coefficient, can be benchmarked.
+Finally, due to the equivalent physics involved (electron-
+ion collisions in dense plasma environments [26]), our
+results on free-free absorption will inform models for
+swift ion stopping in warm dense matter as well as
+corresponding electron-ion equilibration times.
+A.
+Experimental setup
+A sketch of the experimental setup is shown in Fig. 4.
+We will use 184 out of the 192 NIF laser beams to heat
+a gold Hohlraum creating a quasi-thermal radiation field
+that implodes a layered fuel capsule at the center of the
+Hohlraum.
+The capsule is comprised of a 57 µm thick
+beryllium ablator shell, containing a 83 µm thick layer of
+cryogenic solid hydrogen.
+The temporally shaped radiation field created by the
+laser drive will ablate the Be shell and, hence, accelerate
+the payload inward.
+Upon stagnation, a high density
+hydrogen layer with ρ > 100 g cm−3 is formed while most
+of the Be ablator has been ablated.
+The
+implosion
+design
+is
+derived
+from
+inertial
+confinement fusion (ICF) implosions at the NIF [54]
+and applies a well-tested model that matched a variety
+of spherical DT implosion experiments in NIF’s ICF
+
+5
+FIG. 4. Schematic of the experimental setup. Using NIF’s
+laser beams, a nearly Planckian x-ray bath (see bottom right)
+is created by heating a gold Hohlraum with a fuel capsule
+at its center. Upon stagnation, the solid hydrogen layer is
+compressed to mass densities larger than 100 g cm−3.
+Two
+Hohlraum windows allow for measuring the transmission of
+high density hydrogen using x rays created in a stagnating
+plasma inside the backlighter tube. Fielding NIF’s Crystal
+Backlighter Imager [52] and the single line-of-sight (SLOS)
+detector [53] enables us to acquire narrow bandwidth high-
+resolution radiography images of the implosion.
+program. [54, 55] In contrast to ICF implosions aiming for
+high neutron yield,[56] the peak radiation temperature
+of our Hohlraum drive (Trad = 170 eV) is significantly
+reduced, deliberately slowing down the implosion to ∼
+200 km s−1 with the goal of creating extreme densities
+(∼ 150 g cm−3) at moderate temperatures (∼ 200 eV)
+while reducing x-ray and neutron-related background
+signals near stagnation that would affect the radiography
+measurement. These conditions are directly relevant to
+the interiors of red dwarfs.
+The dense plasma states will be probed by x-ray line
+emission, which is created by the eight remaining NIF
+beams that heat a backlighter tube.
+We will perform
+2D-imaging radiography of the implosion and stagnation
+phase using two different photon energies by varying
+the backlighter tube material. Vanadium will result in
+5.2 keV line emission from 1s2p→1s2 (He-α) transitions
+of helium-like ions. In the same way, helium-like cobalt
+ions will produce 7.2 keV photons.
+NIF’s Crystal Backlighter Imager (CBI) system [52]
+will allow for high-resolution, nearly monochromatic
+radiography images of the imploding and stagnating
+sphere. A gated single-line-of-sight (SLOS) detector [53]
+will provide four images per implosion with a time delay
+of ∼ 100 ps between consecutive images.
+From the
+radiography images, we will infer radial profiles of the
+opacity through Abel inversion [57, 58] and forward
+fitting methods.
+FIG.
+5.
+(a)
+1D
+radiation-hydrodynamics
+simulations
+performed using the HYDRA code, [59] showing the mass
+density ρ at a given radius r and time t.
+Our experiment
+intends
+to
+probe
+around
+stagnation
+when
+the
+highest
+fuel compression is predicted.
+Density, temperature, and
+ionization profiles around this time (∼ 11.5 ns after the start
+of the drive laser) are plotted in (b) and predict hydrogen
+mass densities in excess of 150 g cm−3 in the HT mixture with
+a molar mass of 2.5 g mol−1.
+B.
+Radiation hydrodynamic simulations
+The reduced implosion velocity minimizes the hot
+spot x-ray emission at stagnation to improve the signal-
+to-noise ratio of the physics measurements.
+For the
+same reason, we use a (25 %/75 %) HT mixture (which
+is hydrodynamically equivalent to 50 %/50 % DT) for
+the ice layer to minimize the neutron yield and the
+related background signals.
+Tritium is required to
+enable the hydrogen ice layer formation through beta
+layering, where self-heating from beta decay leads to
+a redistribution of HT ice with time. [60–62] Figure 5
+shows an overview of the ∼ 11 ns implosion trajectory
+simulated with HYDRA-1D. [59] Compared to previous
+ICF experiments with Be shells, [54] the ablator thickness
+is reduced to 57 µm to decrease the remaining ablator
+mass to near zero, which will maximize the radiography
+contrast of the hydrogen layer.
+Figure 5(b) illustrates
+examples of radial density, ionization, and temperature
+profiles predicted by hydrodynamic simulations.
+The
+high-density portion of the profiles consists of hydrogen
+(HT) only.
+Our simulations predict that the material
+is compressed to mass densities exceeding 150 g cm−3,
+which corresponds to electron densities of 3.6×1025 cm−3,
+
+6
+FIG. 6. Beryllium content of the capsule close to stagnation
+as a function of time t and radius r. The dash-dotted dark
+line shows the interface of ablator and fuel for a simulation
+without mixing. The dashed lines depict contours of constant
+density in the highly compressed HT. For the times we intend
+to probe (around −0.4 ns to −0.2 ns), the Be is not predicted
+to contaminate this dense part of the fuel. The values on the
+abscissa are given relative to the time where the rebounding
+shock wave coincides with the fuel-ablator interface.
+at a temperature of ∼ 200 eV. These parameters result in
+Fermi energies of ∼ 400 eV and, thus, ∼ 2× larger than
+the thermal energies. Hence, we will probe degenerate
+plasma conditions as expected in the interiors of red
+dwarf stars. In addition, these conditions are expected
+to limit the influence of temperature on the free-free
+absorption, since the 1/
+√
+T term in the expression for
+the inverse bremsstrahlung [Eq. (2)] can be replaced
+approximately by 1/√TF , where TF denotes the Fermi
+temperature. This behavior is supported by the results
+from DFT-MD and the Average Atom Compared to
+previous ICF experiments with Be shells, [54] the ablator
+thickness is reduced to 57 µm to decrease the remaining
+ablator mass to near zero, model, which indicates that
+the opacity is more sensitive to the Fermi temperature
+than the electronic temperature under dense degenerate
+plasma conditions (see Fig. 3 and inset).
+The weak
+dependence on T is highly beneficial for the analysis and
+interpretation of our data, as we can determine opacity
+and from there infer density, while a direct measurement
+of temperature would require additional diagnostics – for
+example x-ray Thomson scattering. [63]
+Reducing the ablator shell thickness and decreasing
+the remaining mass at stagnation might come with
+increased
+risk
+of
+hydrodynamic
+instability
+at
+the
+ablator-ice interface and ablator material mixing into
+the compressed ice layer.
+For a more quantitative
+estimate of mixing, we have performed 1D capsule-only
+simulations using a buoyancy-drag mix model, [64] which
+was successful in explaining experimental performance
+observations of previous layered Be implosions. [54] In
+addition, more recently the buoyancy-drag mix model has
+been calibrated in a focused series of experiments using a
+thin ice layer of varying thickness and detecting neutronic
+signatures of deuterated plastic, originally located near
+the inside of a plastic shell, mixing through the ice
+layer into the hot spot. [65] Figure 6 shows the results
+for our significantly slower implosion design in terms of
+atomic Be fraction as function of radius and time. The
+demarcation line between the Be ablator and the HT ice
+is indicated as a dot-dashed line. We have labeled the
+time of minimum radius of this interface by tmin, which
+coincides with the time when the rebounding shock wave,
+which leads to the formation of the high-compression
+HT ice, passes this interface.
+Our simulations clearly
+show that Be does not mix into the high-compression
+HT ice layer. The radiography measurements are aimed
+to record transmission images between 400 and 200 ps
+before tmin, which, hence, is not affected by Be mixing
+into the high compression HT ice layer.
+IV.
+SIMULATED RADIOGRAPHY SIGNAL
+Synthetic radiography images (see Fig. 7 and the
+appendix for more details) show a clear limb feature at
+the boundary of the central hydrogen and the beryllium
+layer. Applying mass conservation, this feature will be
+used as constraint for the density of the encapsulated
+hydrogen at smaller radii as the total initial fuel mass can
+be accurately characterized. Toward the outer edges of
+the radiography field-of-view of 600×600 µm2, we expect
+the plasma to become fully transmissive to the probe
+radiation, which will be used to normalize the opacities
+measured at smaller radii and obtain absolute values of
+the radial absorption coefficient.
+In the investigated density and temperature regime,
+opacity due to Thomson scattering is expected to reach
+similar values as free-free absorption. As absorption due
+to Thomson scattering scales linearly with ne and free-
+free opacity with n2
+e, this effect can become particularly
+significant in the lower density regions of the imploded
+capsule.
+To disentangle both mechanisms, we will
+perform the absorption measurements at two photon
+energies (5.2 keV and 7.2 keV as described above). While
+disagreeing in the actual magnitude, all but the classical
+approach (gff = 1) presented in Fig. 3 find the same
+proportionality of the free-free opacity with ∼ 1/(hν)(7/2)
+for high photon energies hν. Classically, the Thomson
+cross-section is in fist order independent of probing
+frequency and temperature, which would allow us to
+separate the two contributions to the signal. While this
+assumption might give a reasonable first estimate, our
+AA-MF simulations (see Fig. 3) indicate in accordance
+with previous calculations by Boercker [18] that this
+description as a constant is not applicable at the extreme
+conditions we intend to probe.
+However, models of
+the Thomson scattering have to provide only the ratio
+between the cross-section at the two backlighter energies
+
+7
+FIG. 7.
+(a) Simulated detector image including free-free
+(AA-MF calculations) and bound-free [66] absorption as well
+as Thomson scattering [18] for 5.2 keV (top) and 7.2 keV
+(bottom) backlighter energy.
+The colorbar indicates the
+expected number of photons per pixel.
+Albeit the limited
+temporal and spatial resolution of the detector, the interface
+between the HT mixture and the beryllium ablator is
+predicted to be visible at least for the lower energy.
+(c)
+Absorption coefficient profiles and (b) integrated total capsule
+transmission T for a 5.2 keV backlighter close to the time
+where the highest density in the hydrogen is reached. As the
+lower figure shows, different models for the free-free opacity
+result in notable changes of the total transmission.
+All
+presented plots assume a perfectly symmetrical implosion, no
+mixing between fuel and ablator and a beryllium layer without
+impurities.
+to enable us to differentiate the former from inverse
+bremsstrahlung.
+Regardless of the model applied, the
+Thomson scattering’s contribution to the overall opacity
+might also be used as an additional density constraint
+next to measuring the ablator-hydrogen interface and
+applying mass conservation.
+Further constraints on the implosion parameters will
+be deduced from measuring multiple absorption images
+at different times during the implosion in one shot. The
+stagnation phase is usually well modeled by a self-similar
+description of the conservation laws, [67] which only
+allows certain shapes and time evolutions of the density
+profiles.
+V.
+CONCLUSIONS
+In summary, we presented a concept to leverage
+NIF’s unique capabilities to investigate the deep interiors
+of red dwarf stars in the laboratory and shed light
+on their internal energy transports mechanisms.
+The
+proposed experiment has been accepted within NIF’s
+Discovery Science Program for upcoming shot days in
+2022 and 2023.
+The resulting measurement of free-
+free absorption and opacity will provide a benchmark
+for numerical and analytical approaches, which will in
+turn yield an improved description of the Gaunt factor.
+Finally, interior structure models for massive hydrogen-
+rich astrophysical objects, such as red dwarfs, can be
+revisited on the basis of the new opacity constraint.
+ACKNOWLEDGMENTS
+M.B.
+was
+supported
+by
+the
+European
+Horizon
+2020 programme within the Marie Skłodowska-Curie
+actions (xICE grant number 894725).
+J.L. and D.K.
+acknowledge support by the Helmholtz Association
+under VH-NG-1141 and by GSI Helmholtzzentrum
+für Schwerionenforschung, Darmstadt as part of the
+R&D project SI-URDK2224 with the University of
+Rostock.
+The work of S.S. and D.K. was supported
+by Deutsche Forschungsgemeinschaft (DFG – German
+Research Foundation) project no. 495324226. The work
+of B.B., L.D., G.N.H., S.F.K., N.I., O.L.L., S.A.M,
+L.M., M.O.S., P.A.S. and T.D. was performed under the
+auspices of the DOE by Lawrence Livermore National
+Laboratory under Contract No. DE-AC52-07NA27344.
+R.R. and M.S. acknowledge support from the DFG via
+the Research Unit FOR 2440. The DFT-MD calculations
+were performed at the North-German Supercomputing
+Alliance (HLRN) facilities and at the IT- and Media
+Center of the University of Rostock.
+AUTHOR DECLARATIONS
+Conflict of interest
+The authors have no conflicts of interest.
+
+8
+DATA AVAILABILITY
+The data that support the findings of this study
+are available from the corresponding authors upon
+reasonable request.
+Appendix A: MESA Simulations
+Profiles of temperature, density, and pressure inside
+stars with various masses were calculated using the
+“Modules for Experiments in Stellar Astrophysics” code
+(MESA, release r15140). [6–10] We used the default
+MESA equation-of-state (EOS) which is a blend of
+the OPAL, [68] SCVH, [69] FreeEOS, [70] HELM, [71]
+and PC [72] EOSes.
+Radiative opacities are primarily
+from OPAL, [73, 74] with low-temperature data from
+Ferguson et al. [75] and the high-temperature, Compton-
+scattering dominated regime by Buchler and Yueh. [76]
+Electron conduction opacities are from Cassisi et al.. [77]
+Nuclear reaction rates are from JINA REACLIB [78]
+plus additional tabulated weak reaction rates. [79–81]
+Screening is included via the prescription of Chugunov
+et al.. [82] Thermal neutrino loss rates are from Itoh et
+al.. [83]
+A pre-main-sequence model has been calculated from
+initial parameters of helium mass fraction Yi = 0.2744,
+metallicity Zi
+= 1 − Xi − Yi
+= 0.01913 (with Xi
+being the initial mass fraction of hydrogen), mixing
+length parameter αMLT = 1.9179, and including element
+diffusion, which has been found to reproduce the solar
+model well. [6] The ratio of elements heavier than helium
+was taken from Grevesse and Sauval. [84] The time span
+of the simulation was chosen so that the star spent a
+considerable amount of time on the main sequence. For
+stars smaller than the Sun, 10 times the age of the star
+when the main sequence was entered has been chosen;
+masses M > M⊙ were evolved until tnuc/2 was reached,
+were tnuc = (M/M⊙)−2.9 ×1010 a is an approximation for
+the lifetime of star on the main sequence. [85]
+The decision whether regions of a star were considered
+convective or radiative was based on the Schwarzschild
+criterion.
+Appendix B: Comparing radiative and conductive
+opacities
+The relation between thermal conductivity through
+photon transport (radiation) λrad and the opacity κrad
+is given by
+λrad = 4acT 3
+3ρκrad
+(B1)
+where T is the temperature, ρ is the density, a = 7.5657×
+10−16 Jm−3K−4 is the radiation density constant, and c is
+the speed of light. [17, 85] Eq. (B1) can be used to define
+a conductive opacity κc from the thermal conductivity
+due to electrons λc by analogy.
+This quantity – as
+calculated by Hayashi et al.
+who reproduce the work
+of Mestel [86] and Lee [87] – has been plotted in Fig. 2
+to compare it with radiative opacities.
+As
+the
+two
+contributions
+to
+the
+full
+thermal
+conductivity are additive, the total opacity κtot is given
+by 1/κtot = 1/κrad + 1/κc, i.e., in order for κc being the
+dominant contribution to the total opacity (see the high
+density and low temperature corner of Fig. 2), the former
+quantity has to be small compared to κrad. [85]
+Appendix C: Radiography predictions
+In order to generate the transmission profiles [see
+Fig. 7 (b)] from extinction coefficient line-outs [Fig. 7 (c)],
+we assumed a perfect, spherically symmetric implosion
+and a uniform and monochromatic backlighter emitting
+parallel x rays. We calculated
+Tν = exp
+�
+−
+�
+dxκν(x)ρ(x)
+�
+(C1)
+where the integral runs over the path of the light
+and might, therefore, probe different temperature and
+density conditions. To account for the limited temporal
+resolution of the detector, a series of one-dimensional
+transmission profiles at different times was convolved
+with a Gaussian gate-function (35 ps FWHM). The
+resulting line-out has been rotated,
+and a spatial
+blur in the form of a two-dimensional Gaussian with
+10 µm FWHM in both directions was applied before
+the transmission has been multiplied with the expected
+backlighter photon flux (240 µm−2 ps−1 (Eph = 5.2 keV)
+or 288 µm−2 ps−1 (Eph
+=
+7.2 keV) at the target’s
+position), corrected for attenuators shielding various
+components and re-binned to the pixel-size of the
+detector.
+In a last step, noise proportional to the
+individual pixels’ intensity has been applied to the data.
+[1] I. N. Reid and S. L. Hawley, New Light on Dark Stars
+(Springer Berlin-Heidelberg, 2005).
+[2] M. J. Heath, L. R. Doyle, M. M. Joshi,
+and R. M.
+Haberle, Origins of Life and Evolution of the Biosphere
+
+9
+29, 405 (1999).
+[3] D. E. Osterbrock, Astrophysical Journal 118, 529 (1953).
+[4] J. E. Bailey, T. Nagayama, G. P. Loisel, G. A. Rochau,
+C. Blancard, J. Colgan, P. Cosse, G. Faussurier, C. J.
+Fontes, F. Gilleron, I. Golovkin, S. B. Hansen, C. A.
+Iglesias, D. P. Kilcrease, J. J. MacFarlane, R. C. Mancini,
+S. N. Nahar, C. Orban, J. C. Pain, A. K. Pradhan,
+M. Sherrill, and B. G. Wilson, Nature 517, 56 (2015).
+[5] N. Vinyoles, A. M. Serenelli, F. L. Villante, S. Basu,
+J. Bergström,
+M. C. Gonzalez-Garcia,
+M. Maltoni,
+C. Peña Garay, and N. Song, Astrophysical Journal 835,
+202 (2017).
+[6] B. Paxton, L. Bildsten, A. Dotter, F. Herwig, P. Lesaffre,
+and F. Timmes, ApJS 192, 3 (2011).
+[7] B. Paxton, M. Cantiello, P. Arras, L. Bildsten, E. F.
+Brown, A. Dotter, C. Mankovich, M. H. Montgomery,
+D. Stello, F. X. Timmes, and R. Townsend, ApJS 208,
+4 (2013).
+[8] B. Paxton, P. Marchant, J. Schwab, E. B. Bauer,
+L. Bildsten, M. Cantiello, L. Dessart, R. Farmer, H. Hu,
+N. Langer, R. H. D. Townsend, D. M. Townsley,
+and
+F. X. Timmes, ApJS 220, 15 (2015).
+[9] B. Paxton,
+J. Schwab,
+E. B. Bauer,
+L. Bildsten,
+S. Blinnikov, P. Duffell, R. Farmer, J. A. Goldberg,
+P. Marchant, E. Sorokina, A. Thoul, R. H. D. Townsend,
+and F. X. Timmes, ApJS 234, 34 (2018).
+[10] B.
+Paxton,
+R.
+Smolec,
+J.
+Schwab,
+A.
+Gautschy,
+L. Bildsten, M. Cantiello, A. Dotter, R. Farmer, J. A.
+Goldberg, A. S. Jermyn, S. M. Kanbur, P. Marchant,
+A. Thoul, R. H. D. Townsend, W. M. Wolf, M. Zhang,
+and F. X. Timmes, ApJS 243, 10 (2019).
+[11] R. Kippenhahn, A. Weigert,
+and A. Weiss, Stellar
+Structure
+and
+Evolution
+(Springer
+Berlin-Heidelber,
+2012).
+[12] H. W. Babcock, The Astrophysical Journal 133, 572
+(1961).
+[13] E. N. Parker, The Astrophysical Journal 198, 205 (1975).
+[14] M. Route, The Astrophysical Journal 830, L27 (2016).
+[15] R. O. P. Loyd, E. L. Shkolnik, A. C. Schneider, T. S.
+Barman, V. S. Meadows, I. Pagano,
+and S. Peacock,
+The Astrophysical Journal 867, 70 (2018).
+[16] F.
+Graziani,
+M.
+P.
+Desjarlais,
+R.
+Redmer,
+and
+S. B. Trickey, eds., Frontiers and Challenges in Warm
+Dense Matter (Springer Cham, Heidelberg, New York,
+Dordrecht, London, 2014).
+[17] C. Hayashi, R. Hoshi,
+and D. Sugimoto, Progress of
+Theoretical Physics Supplements 22, 1 (1962).
+[18] D. B. Boercker, The Astrophysical Journal 316, L95
+(1987).
+[19] W. D. Watson, The Astrophysical Journal 158, 303
+(1969).
+[20] I. Hubeny and D. Mihalas, Theory of stellar atmospheres:
+An introduction to astrophysical non-equilibrium quanti-
+tative spectroscopic analysis (Princeton University Press,
+2014).
+[21] D. D. Clayton, Principles of Stellar Evolution and
+Nucleosynthesis
+(The
+University
+of
+Chicago
+Press,
+Chicago and London, 1983).
+[22] H. A. Kramers, Philosophical Magazine 46, 836 (1923).
+[23] J. A. Gaunt, Philosophical Transactions of the Royal
+Society A 229, 163 (1930).
+[24] J. Meyer-ter Vehn and R. Ramis, Physics of Plasmas 26,
+113301 (2019).
+[25] D. O. Gericke, M. S. Murillo, and M. Schlanges, Physical
+Review E 65, 036418 (2002).
+[26] A. Grinenko and D. O. Gericke, Physical Review Letters
+103, 065005 (2009).
+[27] A. Wierling, T. Millat, G. Röpke,
+and R. Redmer,
+Physics of Plasmas 8, 3810 (2001).
+[28] C. E. Starrett, High Energy Density Physics 25, 8 (2017).
+[29] M.
+Bethkenhagen,
+B.
+B.
+L.
+Witte,
+M.
+Schörner,
+G. Röpke, T. Döppner, D. Kraus, S. H. Glenzer, P. A.
+Sterne,
+and R. Redmer, Physical Review Research 2,
+023260 (2020).
+[30] P. A. M. van Hoof,
+R. J. R. Williams,
+K. Volk,
+M. Chatzikos, G. J. Ferland, M. Lykins, R. L. Porter,
+and Y. Wang, Monthly Notices of the Royal Astronomical
+Society 444, 420 (2014).
+[31] P. A. M. van Hoof, G. J. Ferland, R. J. R. Williams,
+K. Volk, M. Chatzikos, M. Lykins,
+and R. L. Porter,
+Monthly Notices of the Royal Astronomical Society 449,
+2112 (2015).
+[32] A. Becker, W. Lorenzen, J. J. Fortney, N. Nettelmann,
+M. Schöttler,
+and R. Redmer, Astrophysical Journal
+Supplement Series 215, 21 (2014).
+[33] A. Becker, M. Bethkenhagen, C. Kellermann, J. Wicht,
+and R. Redmer, Astron. J. 156, 149 (2018).
+[34] B. Holst, M. French, and R. Redmer, Phys. Rev. B 83,
+235120 (2011).
+[35] G. Kresse and J. Hafner, Physical Review B 47, 558
+(1993).
+[36] G. Kresse and J. Hafner, Physical Review B 49, 14251
+(1994).
+[37] G. Kresse and J. Furthmüller, Computational Materials
+Science 6, 15 (1996).
+[38] G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169
+(1996).
+[39] A. Baldereschi, Physical Review B 7, 5212 (1973).
+[40] S. Nosé, J. Chem. Phys. 81, 511 (1984).
+[41] R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957).
+[42] D. A. Greenwood, Proc. Phys. Soc. 71, 585 (1958).
+[43] C. E. Starrett and D. Saumon, Physical Review E 87,
+013104 (2013).
+[44] C. E. Starrett, J. Daligault,
+and D. Saumon, Physical
+Review E 91, 013104 (2015).
+[45] C. E. Starrett and D. Saumon, Physical Review E 93,
+063206 (2016).
+[46] N. Shaffer, N. Ferris, J. Colgan, D. Kilcrease,
+and
+C. Starrett, High Energy Density Physics 23, 31 (2017).
+[47] W. J. Karzas and R. Latter, The Astrophysical Journal
+Supplement Series 6, 167 (1961).
+[48] A. M. Serenelli, W. C. Haxton,
+and C. Peña Garay,
+Astrophysical Journal 743, 24 (2011).
+[49] E. I. Moses, R. N. Boyd, B. A. Remington, C. J. Keane,
+and R. Al-Ayat, Physics of Plasmas 16, 041006 (2009).
+[50] A. L. Kritcher, D. C. Swift, T. Döppner, B. Bachmann,
+L. X. Benedict, G. W. Collins, J. L. DuBois, F. Elsner,
+G. Fontaine, J. A. Gaffney, S. Hamel, A. Lazicki, W. R.
+Johnson, N. Kostinski, D. Kraus, M. J. MacDonald,
+B. Maddox, M. E. Martin, P. Neumayer, A. Nikroo,
+J. Nilsen, B. A. Remington, D. Saumon, P. A. Sterne,
+W. Sweet, A. A. Correa, H. D. Whitley, R. W. Falcone,
+and S. H. Glenzer, Nature 584, 51 (2020).
+[51] D. Kraus, T. Döppner, A. L. Kritcher, A. Yi, K. Boehm,
+B. Bachmann, L. Divol, L. B. Fletcher, S. H. Glenzer,
+O. L. Landen, N. Masters, A. M. Saunders, C. Weber,
+R. W. Falcone,
+and P. Neumayer, J. Phys. Conf. Ser.
+
+10
+717, 012067 (2016).
+[52] G. N. Hall, C. M. Krauland, M. S. Schollmeier, G. E.
+Kemp, J. G. Buscho, R. Hibbard, N. Thompson, E. R.
+Casco, M. J. Ayers, S. L. Ayers, N. B. Meezan, L. F. B.
+Hopkins, R. Nora, B. A. Hammel, L. Masse, J. E. Field,
+D. K. Bradley, P. Bell, O. L. Landen, J. D. Kilkenny,
+D. Mariscal, J. Park, T. J. McCarville, R. Lowe-Webb,
+D. Kalantar, T. Kohut,
+and K. Piston, Review of
+Scientific Instruments 90, 013702 (2019).
+[53] K. Engelhorn, T. J. Hilsabeck, J. Kilkenny, D. Morris,
+T. M. Chung, A. Dymoke-Bradshaw, J. D. Hares, P. Bell,
+D. Bradley, A. C. Carpenter, M. Dayton, S. R. Nagel,
+L. Claus, J. Porter, G. Rochau, M. Sanchez, S. Ivancic,
+C. Sorce,
+and W. Theobald, Review of Scientific
+Instruments 89, 10g123 (2018).
+[54] A. B. Zylstra,
+S. MacLaren,
+S. A. Yi,
+J. Kline,
+D. Callahan, O. Hurricane, B. Bachmann, G. Kyrala,
+L. Masse, P. Patel, J. E. Ralph, J. Salmonson, P. Volegov,
+and C. Wilde, Physics of Plasmas 26, 052707 (2019).
+[55] A. L. Kritcher, D. Clark, S. Haan, S. A. Yi, A. B. Zylstra,
+D. A. Callahan, D. E. Hinkel, L. F. Berzak Hopkins, O. A.
+Hurricane, O. L. Landen, S. A. MacLaren, N. B. Meezan,
+P. K. Patel, J. Ralph, C. A. Thomas, R. Town, and M. J.
+Edwards, Phys. Plasmas 25, 056309 (2018).
+[56] A. B. Zylstra, O. A. Hurricane, D. A. Callahan, A. L.
+Kritcher,
+J. E. Ralph,
+H. F. Robey,
+J. S. Ross,
+C. V. Young, K. L. Baker, D. T. Casey, T. Döppner,
+L. Divol, M. Hohenberger, S. Le Pape, A. Pak, P. K.
+Patel, R. Tommasini, S. J. Ali, P. A. Amendt, L. J.
+Atherton, B. Bachmann, D. Bailey, L. R. Benedetti,
+L. Berzak Hopkins, R. Betti, S. D. Bhandarkar, J. Biener,
+R. M. Bionta,
+N. W. Birge,
+E. J. Bond,
+D. K.
+Bradley,
+T. Braun,
+T. M. Briggs,
+M. W. Bruhn,
+P. M. Celliers,
+B. Chang,
+T. Chapman,
+H. Chen,
+C. Choate, A. R. Christopherson, D. S. Clark, J. W.
+Crippen, E. L. Dewald, T. R. Dittrich, M. J. Edwards,
+W. A. Farmer, J. E. Field, D. Fittinghoff, J. Frenje,
+J. Gaffney, M. Gatu Johnson, S. H. Glenzer, G. P.
+Grim, S. Haan, K. D. Hahn, G. N. Hall, B. A. Hammel,
+J. Harte, E. Hartouni, J. E. Heebner, V. J. Hernandez,
+H. Herrmann, M. C. Herrmann, D. E. Hinkel, D. D.
+Ho, J. P. Holder, W. W. Hsing, H. Huang, K. D.
+Humbird, N. Izumi, L. C. Jarrott, J. Jeet, O. Jones, G. D.
+Kerbel, S. M. Kerr, S. F. Khan, J. Kilkenny, Y. Kim,
+H. Geppert Kleinrath, V. Geppert Kleinrath, C. Kong,
+J. M. Koning, J. J. Kroll, M. K. G. Kruse, B. Kustowski,
+O. L. Landen, S. Langer, D. Larson, N. C. Lemos,
+J. D. Lindl, T. Ma, M. J. MacDonald, B. J. MacGowan,
+A. J. Mackinnon, S. A. MacLaren, A. G. MacPhee,
+M. M. Marinak, D. A. Mariscal, E. V. Marley, L. Masse,
+K. Meaney, N. B. Meezan, P. A. Michel, M. Millot, J. L.
+Milovich, J. D. Moody, A. S. Moore, J. W. Morton,
+T. Murphy, K. Newman, J.-M. G. Di Nicola, A. Nikroo,
+R. Nora, M. V. Patel, L. J. Pelz, J. L. Peterson, Y. Ping,
+B. B. Pollock, M. Ratledge, N. G. Rice, H. Rinderknecht,
+M. Rosen, M. S. Rubery, J. D. Salmonson, J. Sater,
+S. Schiaffino, D. J. Schlossberg, M. B. Schneider, C. R.
+Schroeder, H. A. Scott, S. M. Sepke, K. Sequoia, M. W.
+Sherlock, S. Shin, V. A. Smalyuk, B. K. Spears, P. T.
+Springer, M. Stadermann, S. Stoupin, D. J. Strozzi, L. J.
+Suter, C. A. Thomas, R. P. J. Town, E. R. Tubman,
+C. Trosseille, P. L. Volegov, C. R. Weber, K. Widmann,
+C. Wild, C. H. Wilde, B. M. Van Wonterghem, D. T.
+Woods, B. N. Woodworth, M. Yamaguchi, S. T. Yang,
+and G. B. Zimmerman, Nature 601, 542 (2022).
+[57] K. Hanson, Lect. Notes in Pure and Appl. Math. 115,
+363 (1989).
+[58] M. Howard, M. Fowler, A. Luttman, S. E. Mitchell, and
+M. C. Hock, SIAM Journal on Scientific Computing 38,
+B396 (2016).
+[59] M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones,
+D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan,
+Physics of Plasmas 8, 2275 (2001).
+[60] S. H. Glenzer,
+D. A. Callahan,
+A. J. MacKinnon,
+J. L. Kline, G. Grim, E. T. Alger, R. L. Berger,
+L.
+A.
+Bernstein,
+R.
+Betti,
+D.
+L.
+Bleuel,
+T.
+R.
+Boehly,
+D. K. Bradley,
+S. C. Burkhart,
+R. Burr,
+J. A. Caggiano, C. Castro, D. T. Casey, C. Choate,
+D. S. Clark, P. Celliers, C. J. Cerjan, G. W. Collins,
+E. L. Dewald, P. DiNicola, J. M. DiNicola, L. Divol,
+S. Dixit, T. Döppner, R. Dylla-Spears, E. Dzenitis,
+M. Eckart, G. Erbert, D. Farley, J. Fair, D. Fittinghoff,
+M. Frank, L. J. A. Frenje, S. Friedrich, D. T. Casey,
+M. Gatu Johnson, C. Gibson, E. Giraldez, V. Glebov,
+S. Glenn, N. Guler, S. W. Haan, B. J. Haid, B. A.
+Hammel, A. V. Hamza, C. A. Haynam, G. M. Heestand,
+M. Hermann, H. W. Hermann, D. G. Hicks, D. E. Hinkel,
+J. P. Holder, D. M. Holunda, J. B. Horner, W. W.
+Hsing, H. Huang, N. Izumi, M. Jackson, O. S. Jones,
+D. H. Kalantar, R. Kauffman, J. D. Kilkenny, R. K.
+Kirkwood, J. Klingmann, T. Kohut, J. P. Knauer, J. A.
+Koch, B. Kozioziemki, G. A. Kyrala, A. L. Kritcher,
+J. Kroll, K. La Fortune, L. Lagin, O. L. Landen, D. W.
+Larson, D. LaTray, R. J. Leeper, S. Le Pape, J. D. Lindl,
+R. Lowe-Webb, T. Ma, J. McNaney, A. G. MacPhee,
+T. N. Malsbury, E. Mapoles, C. D. Marshall, N. B.
+Meezan, F. Merrill, P. Michel, J. D. Moody, A. S.
+Moore, M. Moran, K. A. Moreno, D. H. Munro, B. R.
+Nathan, A. Nikroo, R. E. Olson, C. D. Orth, A. E.
+Pak, P. K. Patel, T. Parham, R. Petrasso, J. E. Ralph,
+H. Rinderknecht, S. P. Regan, H. F. Robey, J. S. Ross,
+M. D. Rosen, R. Sacks, J. D. Salmonson, R. Saunders,
+J. Sater, C. Sangster, M. B. Schneider, F. H. Séguin,
+M. J. Shaw, B. K. Spears, P. T. Springer, W. Stoeffl,
+L. J. Suter, C. A. Thomas, R. Tommasini, R. P. J. Town,
+C. Walters, S. Weaver, S. V. Weber, P. J. Wegner, P. K.
+Whitman, K. Widmann, C. C. Widmayer, C. H. Wilde,
+D. C. Wilson, B. Van Wonterghem, B. J. MacGowan,
+L. J. Atherton, M. J. Edwards, and E. I. Moses, Physics
+of Plasmas 19, 056318 (2012).
+[61] A. J. Martin, R. J. Simms,
+and R. B. Jacobs, Journal
+of Vacuum Science & Technology A: Vacuum, Surfaces,
+and Films 6, 1885 (1988).
+[62] M. T. Mruzek, D. L. Musinski, and J. S. Ankney, Journal
+of Applied Physics 63, 2217 (1988).
+[63] S. H. Glenzer and R. Redmer, Reviews of Modern Physics
+81, 1625 (2009).
+[64] G. Dimonte, Physics of Plasmas 7, 2255 (2000).
+[65] B. Bachmann, S. A. MacLaren, S. Bhandarkar, T. Briggs,
+D.
+Casey,
+L.
+Divol,
+T.
+Döppner,
+D.
+Fittinghoff,
+M.
+Freeman,
+S.
+Haan,
+G.
+Hall,
+B.
+Hammel,
+E. Hartouni, N. Izumi, V. Geppert-Kleinrath, S. Khan,
+B. Kozioziemski, C. Krauland, O. Landen, D. Mariscal,
+E. Marley, L. Masse, K. Meaney, A. Moore, A. Pak,
+P. Patel, M. Ratledge, N. Rice, M. Rubery, J. Salmonson,
+J. Sater, D. Schlossberg, M. Schneider, V. A. Smalyuk,
+C. Trosseille, P. Volegov, C. Weber, J. Williams,
+and
+A. Wray, submitted (2022).
+
+11
+[66] D. A. Verner and D. G. Yakovlev, Astronomy and
+Astrophysics Supplement Series 109, 125 (1995).
+[67] S. Atzeni and J. Meyer-ter Vehn, eds., The Physics of
+Inertial Fusion (Clarendon Press, Oxford, 2004).
+[68] F. J. Rogers and A. Nayfonov, The Astrophysical Journal
+576, 1064 (2002).
+[69] D. Saumon, G. Chabrier,
+and H. M. van Horn, The
+Astrophysical Journal Supplement Series 99, 713 (1995).
+[70] A. W. Irwin, “The FreeEOS code for calculating the
+equation of state for stellar interiors,” (2004).
+[71] F. X. Timmes and F. D. Swesty, The Astrophysical
+Journal Supplement Series 126, 501 (2000).
+[72] A. Y. Potekhin and G. Chabrier, Contributions to
+Plasma Physics 50, 82 (2010).
+[73] C. A. Iglesias and F. J. Rogers, The Astrophysical
+Journal 412, 752 (1993).
+[74] C. A. Iglesias and F. J. Rogers, The Astrophysical
+Journal 464, 943 (1996).
+[75] J. W. Ferguson, D. R. Alexander, F. Allard, T. Barman,
+J. G. Bodnarik, P. H. Hauschildt, A. Heffner-Wong, and
+A. Tamanai, The Astrophysical Journal 623, 585 (2005).
+[76] J. R. Buchler and W. R. Yueh, The Astrophysical Journal
+210, 440 (1976).
+[77] S. Cassisi, A. Y. Potekhin, A. Pietrinferni, M. Catelan,
+and M. Salaris, The Astrophysical Journal 661, 1094
+(2007).
+[78] R. H. Cyburt, A. M. Amthor, R. Ferguson, Z. Meisel,
+K. Smith,
+S. Warren,
+A. Heger,
+R. D. Hoffman,
+T. Rauscher, A. Sakharuk, H. Schatz, F. K. Thielemann,
+and M. Wiescher, The Astrophysical Journal Supplement
+Series 189, 240 (2010).
+[79] G. M. Fuller, W. A. Fowler,
+and M. J. Newman, The
+Astrophysical Journal 293, 1 (1985).
+[80] T. Oda, M. Hino, K. Muto, M. Takahara, and K. Sato,
+Atomic Data and Nuclear Data Tables 56, 231 (1994).
+[81] K. Langanke and G. Martínez-Pinedo, Nuclear Physics
+A 673, 481 (2000).
+[82] A. I. Chugunov, H. E. Dewitt,
+and D. G. Yakovlev,
+Physical Review D 76, 025028 (2007).
+[83] N. Itoh, H. Hayashi, A. Nishikawa,
+and Y. Kohyama,
+The Astrophysical Journal Supplement Series 102, 411
+(1996).
+[84] N. Grevesse and A. J. Sauval, Space Science Reviews 85,
+161 (1998).
+[85] C. Hansen,
+S. Kawaler,
+and V. Trimble, Stellar
+Interiors: Physical Principles, Structure, and Evolution,
+Astronomy and Astrophysics Library (Springer New
+York, 2004).
+[86] L. Mestel, Mathematical Proceedings of the Cambridge
+Philosophical Society 46, 331 (1950).
+[87] T. D. Lee, The Astrophysical Journal 111, 625 (1950).
+

1dAzT4oBgHgl3EQfRfuL/content/2301.01217v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:eaf060e6bbbe047d158937323204b8227f55c6c9c8afa89bce6e446ab6bed709
+size 1257432

1dAzT4oBgHgl3EQfRfuL/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f46a98e5a5b9a5433f7298c2c62f13c0847b1e1cd7d595f91613db6b3f12d08a
+size 3211309

1dAzT4oBgHgl3EQfRfuL/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e1126aed6c3c7bf7ef5d49949ed5281e2c255f6682ac71ce44995c435ccf7795
+size 125118

29E1T4oBgHgl3EQf5wUG/content/2301.03514v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c210ac11556216d3310828e94044130ff2845027612479b55e0ced6b3f65e037
+size 515253

29E1T4oBgHgl3EQf5wUG/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:70e2d0cedfd091cab91f624c8bf91cef27a2b0ef26c95401367bdbca96bebfb0
+size 124722

2dFAT4oBgHgl3EQfDhxB/content/2301.08416v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b4e49ed0fcd8cbc68b1ec7260e4e205bb33b4d983783e0b47b52f34c36f310be
+size 1308603

2dFAT4oBgHgl3EQfDhxB/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:472eeac83328726ee5e0e9275323be9e06f1aeb44a169620c8f4e559c06963b8
+size 2752557

2tAzT4oBgHgl3EQf9P4T/content/tmp_files/2301.01915v1.pdf.txt

@@ -0,0 +1,1992 @@
+arXiv:2301.01915v1  [cs.IT]  5 Jan 2023
+CHINA COMMUNICATIONS
+Sum-Rate Maximization in Active RIS-Assisted Multi-Antenna
+WPCN
+Jie Jiang, Bin Lyu, Pengcheng Chen, and Zhen Yang
+School of Communications and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
+Abstract:
+In this paper, we propose an active re-
+configurable intelligent surface (RIS) enabled hybrid
+relaying scheme for a multi-antenna wireless pow-
+ered communication network (WPCN), where the ac-
+tive RIS is employed to assist both wireless energy
+transfer (WET) from the power station (PS) to energy-
+constrained users and wireless information transmis-
+sion (WIT) from users to the receiving station (RS).
+For further performance enhancement, we propose to
+employ both transmit beamforming at the PS and re-
+ceive beamforming at the RS. We formulate a sum-
+rate maximization problem by jointly optimizing the
+RIS phase shifts and amplitude reflection coefficients
+for both the WET and the WIT, transmit and receive
+beamforming vectors, and network resource alloca-
+tion. To solve this non-convex problem, we propose an
+efficient alternating optimization algorithm with linear
+minimum mean squared error criterion, semi-definite
+relaxation (SDR) and successive convex approxima-
+tion techniques. Specifically, the tightness of apply-
+ing the SDR is proved.
+Simulation results demon-
+strate that our proposed scheme with 10 reflecting el-
+ements (REs) and 4 antennas can achieve 17.78% and
+415.48% performance gains compared to the single-
+antenna scheme with 10 REs and passive RIS scheme
+with 100 REs, respectively.
+Keywords: Wireless powered communication net-
+work, active reconfigurable intelligent surface, beam-
+forming, sum-rate maximization.
+Received: XX
+Revised: XX
+Editor: XX
+I. INTRODUCTION
+With the development of the Internet-of-Things (IoT),
+an intelligent society with ubiquitous interconnections
+and deep coverage will be truly realized. However,
+wireless devices (WDs) in IoT networks are generally
+energy-constrained and suffer from limited lifetime
+[1], which fundamentally limits the performance of
+communication networks. Traditional ways of chang-
+ing or recharging the batteries manually are impossi-
+ble and unacceptable, especially when the number of
+WDs is numerous. Therefore, how to tackle this issue
+is a critical problem in the widespread development of
+IoT. Wireless powered communication has been pro-
+posed as a prospective technology for enhancing the
+energy sustainability of WDs, which can be classified
+into two directions based on application scenarios [2–
+4]. The first one focuses on investigating simultane-
+ous wireless information and power transfer (SWIPT),
+where the base station (BS) simultaneously transfers
+energy and information signals to energy receivers
+and information receivers via the common radio fre-
+quency (RF) signals in the downlink (DL), resulting
+in a pivotal tradeoff between the achievable rate and
+harvested energy [5]. In contrast to the SWIPT, wire-
+less powered communication network (WPCN) has
+been proposed as a novel type of wireless network di-
+agram to improve the lifetime of WDs and enhance
+the deployment flexibility of IoT. In a WPCN, energy-
+constrained WDs first harvest energy in the DL and
+then use the harvested energy to transmit independent
+information in the uplink (UL) based on the widely
+used harvest-then-transmit (HTT) protocol [6].
+WPCN has been widely investigated in the literature
+China Communications
+1
+
+[6–9], which promotes the development of WPCN.
+However, WPCN generally suffers from the “doubly
+near-far” phenomenon if the power station (PS) and
+the receiving station (RS) are co-located at the hybrid
+access point (HAP) [6, 8]. Specifically, a WD located
+far away from the HAP harvesting less energy in the
+DL has to transmit information with more power in
+the UL, which results in an unfair time and resource
+allocation among the WDs. To deal with the issue, a
+promising way is to deploy the PS and RS separately
+[10, 11]. In [10], multiple users harvest energy from a
+dedicated PS and then communicate with an informa-
+tion RS following the HTT protocol. In this scenario,
+a user physically close to the PS is naturally far away
+from the RS, and vice versa. Considering a similar
+scenario, a user-centric energy-efficient (EE) problem
+in WPCN is investigated in [11]. However, the perfor-
+mance of WPCN is still limited due to the low efficien-
+cies caused by the severe path-loss, which seriously
+affects its practical applications.
+Recently, reconfigurable intelligent surface (RIS),
+with the unprecedented ability to reshape the wireless
+transmission environment, has drawn widespread at-
+tentions from academia and industry [12–18]. RIS is
+comprised of a large number of programmable reflect-
+ing elements (REs), which can alter the phase shifts
+and amplitudes of incident signals. As such, RIS can
+adaptively modify the impinging radio waves towards
+the appropriate direction [13]. According to the re-
+flection patterns, RIS can be classified as passive RIS
+and active RIS. Without the property of power amplifi-
+cation, the independent diffusive scatterer-based (IDS)
+model accounts for the basic properties of passive RIS,
+which has been widely adopted in RIS-assisted wire-
+less communications [18]. The passive RIS is only
+equipped with the phase-shift controller, while the ac-
+tive RIS contains both the phase-shift controller and
+the active reflection-type amplifier. Hence, the active
+RIS can alter both the phase shifts and amplitudes of
+the incident signals. It is worth noting that the active
+RIS with its novel hardware structure and signal model
+has been proposed in [19, 20].
+Different from the
+full-duplex amplify-and-forward (FD-AF) relay that
+requires power-consuming RF chains, the active RIS
+can directly reflect and amplify the incident signals in
+the EM level in a FD manner without reception. In this
+way, the active RIS exhibits promising qualities, such
+as a low power consumption, light weight, conformal
+geometry and high flexibility for practical deployment.
+Currently, the passive RIS has been widely applied
+in WPCNs for performance enhancement [21–24]. In
+[21], the passive RIS is employed between the HAP
+and users to improve both DL WET and UL WIT effi-
+ciencies in single-input-single-output (SISO) WPCN.
+To achieve further performance improvement, the
+multi-antenna technique is employed in [22], where
+the HAP with multi-antenna transmits energy signals
+to users in the DL and receives information from users
+in the UL by employing transmit bemforming and re-
+ceive beamforming, respectively.
+In [23], the fully
+dynamic RIS beamforming scheme is proposed for
+WPCN, for which the phase shift vectors are indepen-
+dently designed over different time slots. However,
+in the above works [21–23], the PS and RS are also
+co-located at the HAP, which results in performance
+unfair among users.
+To address this issue, the au-
+thors in [24] consider the scenario where the PS and
+RS are separately deployed, for which the locations of
+RIS and users can be carefully considered to achieve a
+fair performance among users. However, as mentioned
+above, the passive RIS can only reflect incident signals
+without amplification, which leads to the limited per-
+formance enhancement due to the double-fading ef-
+fect suffered by the reflecting links. Thus, the energy-
+constrained users still need to consume much time for
+harvesting energy in the DL and have less time for in-
+formation transmission.
+Inspired by the amplification characteristic of the
+active RIS, the active RIS is confirmed to be superior
+to the passive RIS in terms of performance enhance-
+ment, and thus has been considered a promising tech-
+nique for IoT networks [19, 20, 25–29]. The authors
+in [19] compare the capacity improvement achieved
+by the active RIS to the passive RIS, which demon-
+strats that the active RIS can fundamentally mitigate
+the double-fading effect. In [20], an active RIS is ap-
+plied in single input multiple output (SIMO) systems,
+for which the joint optimization of phase shifts ma-
+trix and receive beamforming is considered to obtain
+the maximum achievable rate. In [25], the placement
+of the active RIS is optimized to enhance SISO sys-
+tems’ performance. The authors in [26] propose to use
+the active RIS to achieve secure transmission, which
+not only establishes the reliable link from the trans-
+mitter to the receiver but also prevents the confidential
+information intercepted by the eavesdropper. The ac-
+2
+China Communications
+
+tive RIS-aided multiuser MISO PS-SWIPT is studied
+in [27] to minimize the base station transmit power,
+which shows significant improvements compared to
+the passive RIS-aided system. Similarly, in [28], an
+active RIS is employed to assist SWIPT to boost the
+efficiency of both WET and WIT, while the conclu-
+sions and approaches are inapplicable to the WPCN
+system because of thire different system models.
+Although the active RIS has received a lot of inter-
+ests for wireless communication networks, the appli-
+cations of active RIS in WPCN is still at the very early
+stage and has not been well studied in the literature.
+To the best of our knowledge, there exists only one
+paper investigating the usage of active RIS in WPCN
+[29]. Specifically, the authors in [29] investigate the
+weight sum-rate maximization problem in the active
+RIS assisted single-antenna WPCN, where the PS and
+RS is co-located at the HAP. As a result, similar to
+[21–23], a part of WDs in [29] still suffer from the
+“doubly near-far” phenomenon, which is not suitable
+for practical applications with high requirement of per-
+formance fairness. Moreover, the authors consider a
+certain simplified communication scenario where both
+the HAP and the WDs have single antenna each. The
+transmit beamforming and receive beamforming can-
+not be exploited, which is also a key technology for
+performance enhancement.
+Motivated by the observations above, we propose
+an active RIS enabled hybrid relaying scheme for the
+multi-antenna WPCN, where the active RIS is em-
+ployed to facilitate both the WET from the PS to
+energy-constrained users and the WIT from users to
+the RS, which is shown in Figure 1. Compared with
+the existing works which used the passive RIS in
+WPCN [21–24], our proposed active RIS scheme can
+amplify the energy signals and information signals to
+achieve a satisfying system performance.
+Different
+from the single-antenna scenario considered in [29],
+we propose to employ multi-antenna at both the PS
+and RS, which can construct the transmit beamform-
+ing and receive beamforming for further performance
+enhancement. Specifically, the transmit beamforming
+at the PS can be used to enhance the WPT efficiency
+from the PS to users. In the meanwhile, the receive
+beamforming at the RS can be used to exploit the an-
+tenna gain and eliminate the noise caused by the ac-
+tive RIS. In the considered system setup, we aim to
+maximize the sum-rate problem by jointly optimiz-
+ing the transmit beamforming at the PS, the receive
+beamforming at the RS, the reflecting coefficients at
+the RIS, and network resource allocation. It should
+be noted that compared to [21–24, 29], our formulated
+problem is much more challenging to solve and the
+proposed algorithms in [21–24, 29] cannot be used to
+solve our formulated problem. Thus, we propose an
+efficient algorithm to solve the formulated problem.
+The main contributions of this paper are summarized
+as follows:
+• We propose an active RIS assisted multi-antenna
+WPCN for performance enhancement, where the
+active RIS is served as a hybrid relay to achieve
+two purposes, i.e., the first one is to assist the
+WET from the PS to users, and the second one
+is to aid the WIT from users to the RS. To fur-
+ther improve system performance, both trans-
+mit beamforming and receive beamforming tech-
+niques are respectively considered at the PS and
+RS.
+• We investigate the sum-rate maximization prob-
+lem by jointly optimizing transmit beamforming
+vector at the PS, receive beamforming vectors at
+the RS, phase shifts and amplitude reflection coef-
+ficients at the RIS for both the WET and the WIT,
+and network resource allocation. To deal with the
+non-convexity of the formulated problem, we pro-
+pose an efficient alternating optimization (AO) al-
+gorithm. Specifically, the original problem can be
+divided into four sub-problems, which are solved
+sequentially in an alternating manner until con-
+vergence is achieved.
+• For designing the receive beamforming, we apply
+the linear minimum mean squared error (MMSE)
+criterion and obtain the closed-form expression.
+For the optimization of the transmit beamform-
+ing and RIS reflecting coefficient matrices for
+the WET, the semidefinite relaxation (SDR) tech-
+nique is adopted and the tightness of applying the
+SDR is proved. For the optimization of RIS re-
+flecting coefficients for the WIT, we obtain the
+optimal phase shifts in a closed-form and propose
+a successive convex approximation (SCA) algo-
+rithm to determine the optimal amplitude reflec-
+tion coefficients. In addition, the convergence of
+proposed problem is analyzed and confirmed via
+numerical simulations.
+China Communications
+3
+
+• Finally, numerical results are provided to evaluate
+the performance of proposed scheme, which indi-
+cates that compared to the single-antenna scheme
+with 10 REs and the passive-RIS scheme with 100
+REs, the proposed scheme with 4 antennas and 10
+REs can achieve 17.78% and 415.48% sum-rate
+gain, respectively.
+The rest of this paper is organized as follows. Sec-
+tion II describes the system model of the active RIS-
+assisted multi-antenna WPCN. The sum-rate maxi-
+mization problem is formulated in Section III and
+solved in Section IV, respectively. In Section V, per-
+formance is evaluated by numerical results. Finally,
+this paper is concluded in Section VI.
+Notations: In this paper, vectors and matrices are
+denoted by boldface lowercase and uppercase letters,
+respectively. The operators ( · )T, ( · )H, | · | and ∥ · ∥
+denote the transpose, conjugate transpose, absolute
+value and the Euclidean norm, respectively. Tr( · ) and
+rank( · ) denote the trace and rank of a matrix, respec-
+tively. X ⪰ 0 represents that X is a positive semidef-
+inite matrix. E[ · ] stands for the statistical expecta-
+tion. IN denotes the N-dimensional identity matrix.
+0 denotes the zero matrix/vector with appropriate size.
+CN×M denotes the set of all N × M complex-valued
+matrices. HM denotes the set of all M ×M Hermitian
+matrices. RN×1 represents the set of all N × 1 real-
+valued vectors. CN
+�
+µ, σ2�
+denotes the distribution of
+a circularly symmetric complex Gaussian random vec-
+tor with mean µ and variance σ2. arg( · ) denotes the
+phase extraction operation. diag(x) denotes a diago-
+nal matrix whose diagonal elements are from vector x.
+Im( · ) and Re( · ) respectively denotes the imaginary
+part and real part of a complex number.
+II. SYSTEM MODEL
+As shown in Figure 1, we consider an active RIS-aided
+multi-antenna WPCN, which consists of a PS with M
+antennas, a RS with L antennas, an active RIS, and
+K energy-constrained users each with single antenna.
+We assume that each user is equipped with an energy
+harvesting (EH) circuit for harvesting energy, where
+a rectifier is used to convert the received RF signals
+to direct current (DC) signals. Then, the net energy
+harvested from the DC signals can be stored in the
+rechargeable battery. The active RIS consists of N
+active REs, which can steer the reflected signals in
+��,�
+�
+��,�
+�
+��,�
+��,�
+��
+��
+PS
+RS
+��
+Active RIS
+Energy transfer
+Information transmission
+EH circuit
+Rectifier
+RF signal
+Rechargeable
+battery
+DC signal
+Figure 1.
+System model for an active RIS-assisted multi-
+antenna WPCN.
+a specific direction and also amplify them by the ac-
+tive loads (negative resistance) [20]. In contrast to the
+passive RE, each active RE is equipped with an addi-
+tionally integrated active reflection-type amplifier sup-
+ported by a power supply. By appropriately setting the
+effective resistance, it is reasonable to assume that the
+reflection amplitude and phase of each element is inde-
+pendently [19, 20, 25–29]. To power the operations of
+active RIS and users, the PS is equipped with a stable
+energy source. In addition, the PS has the capability
+for performing computational tasks [21]. In particu-
+lar, the users first harvest energy from the RF signals
+transmitted by the PS and then use the harvested en-
+ergy to deliver information to the RS. To allievate the
+severe path-loss suffered by the reflecting links, the ac-
+tive RIS is employed to improve the WET efficiency
+from the PS to users and the WIT efficiency from the
+users to the RS.
+The channels are assumed to follow a quasi-static
+flat-fading model.
+That is, all channel coefficients
+are constant throughout each transmission block but
+vary from block to block [30]. The downlink base-
+band equivalent channels of PS-to-RIS, RIS-to-Uk,
+and PS-to-Uk links are denoted by Hr ∈ CN×M,
+hH
+u,k ∈ C1×N, and hH
+d,k ∈ C1×M, respectively, where
+Uk denotes the k-th user. Similarly, the uplink base-
+band equivalent channels of Uk-to-RIS, RIS-to-RS,
+and Uk-to-RS links are respectively denoted by gu,k ∈
+CN×1, Gr ∈ CL×N, and gd,k ∈ CL×1, respectively.
+Since there have been many efficient channel estima-
+4
+China Communications
+
+用tion techniques proposed for RIS systems [31–34], we
+assume the perfect channel state information can be
+available in advance, which is a common assumption
+considered in [21, 22, 35] and a prerequisite for inves-
+tigating the upper-bound of system performance. It
+should be noted that the channel estimation error is
+generally inevitable [31]. However, the effect of chan-
+nel estimation error on system performance degrada-
+tion is out the scope of this paper.
+According to the HTT protocol [6], the normalized
+transmission block of interest is divided into K + 1
+time slots. The first time slot with duration of τ0 ∈
+[0, 1] is a dedicated slot for WET, in which all users
+harvest energy from the PS with the assistance of
+active RIS. The remaining K time slots denoted by
+τ = [τ1, . . . , τK], are used for UL WIT via the time di-
+vision multiple access (TDMA) scheme. Specifically,
+during τk, k = 1, · · · , K, Uk delivers its information
+to the RS. Without loss of generality, the whole oper-
+ation time period is set to a normalized transmission
+block. The network time scheduling constraint is thus
+given by
+τ0 +
+K
+�
+k=1
+τk ≤ 1, ∀k.
+(1)
+2.1 Wireless Energy Transfer Phase
+In the WET phase, the PS transmits energy signals to
+all users with the assistance of the active RIS. Denote
+the transmitted signal as s = w0s, where s is the
+pseudo-random baseband signal transmitted by the PS,
+and w0 ∈ CM×1 is the transmit beamforming vector.
+The energy constraint at the PS is expressed as
+E
+�
+|s|2�
+= Tr
+�
+w0wH
+0
+�
+≤ P0,
+(2)
+where P0 denotes the maximum transmit power at the
+PS.
+The reflecting coefficient matrix of the active
+RIS in the WET phase is denoted by Φ0
+=
+diag {φ0,1, . . . , φ0,N}
+∈
+CN×N
+with
+φ0,n
+=
+a0,nejθ0,n, n = 1, . . . , N, where a0,n and θ0,n rep-
+resent the amplitude reflection coefficient and phase
+shift of the n-th RE, respectively. Without loss of gen-
+erality, we suppose each active RE has the following
+constraints
+a0,n ≤ an,max, 0 ≤ θ0,n ≤ 2π, ∀n,
+(3)
+where an,max is the maximum amplitude reflection co-
+efficient of n-th RE. It is worth noting that an,max can
+be greater than 1 [25], which is a main characteris-
+tic distinguishing the active RIS from the passive RIS
+since the active load can amplify the reflected signals.
+The received signal at Uk during τ0 is given by
+yu,k = hH
+d,ks
+� �� �
+direct link
++ hH
+u,kΦ0 (Hrs + nv)
+�
+��
+�
+RIS-aided link
++nu,k, ∀k,
+(4)
+where nu,k ∈ C and nv ∈ CN×1 represent the ad-
+ditive white Gaussian noise (AWGN) at Uk and the
+RIS, respectively. Without loss of generality, we as-
+sume nu,k ∼ CN
+�
+0, σ2
+u,k
+�
+and nv ∼ CN
+�
+0, σ2
+vIN
+�
+.
+Denote the equivalent downlink channel as hH
+k
+=
+hH
+u,kΦ0Hr + hH
+d,k ∈ C1×M and (4) can be rewritten
+as
+yu,k = hH
+k w0s + hH
+u,kΦ0nv + nu,k, ∀k.
+(5)
+Due to the fact that the active RIS not only amplifies
+the desired signal, i.e., s, but also amplifies the input
+noise, i.e., nv, it is reasonable to consider the second
+term of (4) for computing the amount of harvested en-
+ergy accurately [20]. However, the noise at Uk is gen-
+erally quite small and can be negligible. Accordingly,
+the harvested energy by Uk, denoted by Ek, is given
+by
+Ek = β
+��hH
+k w0
+��2τ0 + β
+��hH
+u,kΦ0
+��2σ2
+vτ0, ∀k,
+(6)
+where β ∈ (0, 1] denotes the energy conversion effi-
+ciency of each user. It is practical for us to consider
+the linear EH model here, which is also a common as-
+sumption in the literature [6, 8, 11, 10, 22, 29].
+It is worth noting that the active RIS can allocate
+the available reflecting power to amplify the incident
+signals with active loads [20]. In the DL WET phase,
+the amplification power of s and nv is limited by the
+RIS power budget, which is shown by the following
+constraint
+P0 ∥Φ0Hr∥2 + σ2
+v ∥Φ0IN∥2 ≤ Pr,
+(7)
+where Pr is the maximum reflecting power for ampli-
+fication at the active RIS and substantially lower than
+that of an active RF amplifier [25].
+China Communications
+5
+
+2.2 Wireless Information Transmission Phase
+In the WIT phase, the users utilize the harvested en-
+ergy to transmit information to the RS via a TDMA
+manner. Let fk denotes the information-carrying sig-
+nal of Uk with unit power and then the transmit signal
+during τk is denoted by xk = √pkfk, where pk is the
+transmit power at Uk. We assume that all the harvested
+energy at Uk in the WET phase is used for delivering
+its own information. Let p = [p1, . . . , pK] ∈ R1×K,
+which satisfies
+pkτk ≤ Ek, ∀k.
+(8)
+Similarly, the reflecting coefficient matrix at the
+active RIS for the WIT during τk is denoted by
+Φk = diag {φk,1, . . . , φk,N} ∈ CN×N, where φk,n =
+ak,nejθk,n, ak,n and θk,n have the following constraints
+ak,n ≤ an,max, 0 ≤ θk,n ≤ 2π, ∀k, ∀n.
+(9)
+The received signal at the RS from Uk with the as-
+sistance of active RIS during τk is written as
+yr,k = gH
+d,kxk
+� �� �
+direct link
++ GrΦk (gu,kxk + nv)
+�
+��
+�
+RIS-aided link
++nr, ∀k,
+(10)
+where nr ∈ CL×1 represents the AWGN at the RS and
+satisfies nr ∼ CN
+�
+0, σ2
+rIN
+�
+.
+In the UL WIT phase, we also have the amplification
+power constraint at the active RIS as follows
+pk ∥Φkgu,k∥2 + σ2
+v ∥ΦkIN∥2 ≤ Pr, ∀k.
+(11)
+Denote the receive beamforming vector at the RS
+during τk as wk ∈ CL×1, which can be used to ex-
+tract the desired signal and suppress interference and
+noises. Let the equivalent uplink channel be gk =
+gd,k + GrΦkgu,k, ∀k. The estimated signal at the RS
+during τk is expressed as
+uk =wH
+k yr,k
+=wH
+k gkxk + wH
+k GrΦknv + wH
+k nr, ∀k.
+(12)
+Then, the signal-noise-ratio (SNR) at the RS during
+τk is written as
+γk = pk
+��wH
+k (GrΦkgu,k + gd,k)
+��2
+��wH
+k GrΦk
+��2 σ2v + ∥wk∥2 σ2r
+, ∀k.
+(13)
+Denote the achievable rate from Uk to the RS as Rk,
+which is formulated as
+Rk = τk log (1 + γk) , ∀k.
+(14)
+III. PROBLEM FORMULATION
+In this section, we formulate the system sum-rate max-
+imization problem by jointly optimizing the reflecting
+coefficients for both the WET and the WIT at the ac-
+tive RIS, the transmit beamforming at the PS, the re-
+ceive beamforming at the RS, the transmit power at
+each user, and the network time scheduling. The opti-
+mization problem is formulated as
+(P1)
+max
+τ0,τ,Φ0,Φk,w0,p,wk
+K
+�
+k=1
+Rk
+(15)
+s.t.
+(1), (2), (3), (7), (8), (9) and (11),
+τ0 ≥ 0, τk ≥ 0, pk ≥ 0, ∀k.
+(16)
+where (16) indicates that the time and power variables
+are all nonnegative.
+One can observe that the objective function in (15)
+is a non-concave function due to the coupled of vari-
+ables. In addition, there exists several non-convex con-
+straints, i.e., (2), (7), (8) and (11). It is thus challeng-
+ing to solve P1 directly by standard optimization tech-
+niques. In the next section, we propose an AO algo-
+rithm to solve it efficiently.
+IV. ALTERNATING OPTIMIZATION SO-
+LUTION
+In this section, an efficient AO algorithm is proposed
+to solve P1. In particular, we decompose P1 into sev-
+eral subproblems and iteratively solve them in an al-
+ternating manner. To show the procedure of AO algo-
+rithm, we summarize a flow chart in Figure 2. Specif-
+ically, the variables are partitioned into four blocks,
+{wk}, {w0, τ, p}, {Φ0, τ0, τ, p}, and {Φk}. Then,
+the variables in each block are alternately solved by
+6
+China Communications
+
+Linear MMSE-based Receive 
+Beamforming Optimization
+SDP-based Transmit 
+Beamforming Optimization
+SDP-based RIS Reflecting Coefficients for the 
+WET and Resource Allocation Optimization
+SCA-based RIS Reflecting Coefficients 
+Optimization for the WIT
+System Variables
+�, �, �� , ��
+��, ��, ��
+�, {��}
+{��}
+�� , �� , ��, ��
+��
+�, �
+Discarding
+��, �� , ��
+��, ��,
+�, �
+�, ��
+��
+AO iteration flow
+Update
+Input
+Figure 2. A flow chart of the proposed algorithm.
+its corresponding sub-problem with the other blocks
+fixed until the convergence is achieved.
+4.1 Linear MMSE-based Receive Beamform-
+ing Optimization
+With the other variables fixed, we first design the re-
+ceive beamforming vectors {wk}. To cope with the
+interference caused by nv and nr in (13), we apply
+the linear MMSE criterion here. Based on this crite-
+rion, the MMSE-based receive beamforming is given
+by
+w∗
+k =
+�
+gkgH
+k + σ2
+v
+pk
+GrΦkΦH
+k GH
+r + σ2
+r
+pk
+IL
+�−1
+gk, ∀k.
+(17)
+4.2 SDP-based Transmit Beamforming Opti-
+mization
+We then proceed to optimize {w0, τ, p} with the other
+variables {wk, Φ0, τ0, Φk} fixed. Letting ek = pkτk
+and e = [e1, . . . , eK] and applying the obtained results
+in (17), P1 can be simplified as follows
+(P2) max
+w0,τ,e
+K
+�
+k=1
+τk log
+�
+1 + ǫk
+ek
+τk
+�
+(18)
+s.t.
+ek ≤ Ek, ∀k,
+(19)
+τk ≥ 0, ek ≥ 0, ∀k,
+(20)
+(1), (2) and (11),
+where ǫk
+=
+|(w∗
+k)H(GrΦkgu,k+gd,k)|
+2
+∥(w∗
+k)HGrΦk∥
+2σ2v+∥w∗
+k∥
+2σ2r , ∀k.
+It
+can be found that P2 is highly non-convex.
+To
+solve it efficiently, the SDR technique [36] is em-
+ployed.
+Define Hk
+=
+hkhH
+k , and Gu,k
+=
+diag
+�
+|gu,k,1|2 , |gu,k,2|2 , . . . , |gu,k,N|2�
+,
+∀k.
+Let
+W0
+=
+w0wH
+0 , which satisfies W0
+⪰
+0 and
+rank(W0) = 1. Then, (19) is rewritten as
+ek ≤ βτ0[Tr (HkW0) +
+��hH
+u,kΦ0
+��2 σ2
+v], ∀k.
+(21)
+Denote the RIS reflecting coefficient vector for the
+WET as ϕk = [φk,1, φk,2, . . . , φk,N]T, ∀k, (11) can
+be recast as
+ekϕH
+k Gu,kϕk + τkσ2
+vϕH
+k ϕk ≤ τkPr, ∀k.
+(22)
+Then, P2 can be equivalently transformed into
+(P2-1) max
+W0,τ,e
+K
+�
+k=1
+τk log
+�
+1 + ǫk
+ek
+τk
+�
+(23)
+s.t.
+Tr (W0) ≤ P0,
+(24)
+W0 ⪰ 0,
+(25)
+rank(W0) = 1,
+(26)
+(1), (20), (21) and (22).
+Since the rank-one constraint in (26) is non-convex,
+we employ the SDR technique to relax it. Thus, P2-1
+becomes to be a convex semidefinite program (SDP)
+and can be solved with the interior-point method [37].
+Proposition 1. The optimal transmit beamforming
+matrix obtained by solving the relaxed version of P2-1,
+denoted by W ∗
+0 , is rank-one.
+Proof. Please refer to Appendix A.
+According to Proposition 1, the tightness of SDR
+is guaranteed. Hence, we can employ Cholesky de-
+composition to obtain the optimal energy beamform-
+ing vector w∗
+0.
+4.3 SDP-based RIS Reflecting Coefficients for
+the WET and Resource Allocation Opti-
+mization
+In this sub-section, we focus on optimizing the re-
+flecting beamforming at the RIS in the WET phase,
+the transmit power at each user, and the network
+time scheduling.
+Since τ0 and Φ0 are coupled,
+we first optimize {Φ0, τ, p} with τ0 given. Define
+Ψ0 = ˜ϕ0 ˜ϕH
+0 with Ψ0 ⪰ 0 and rank(Ψ0) = 1,
+where ˜ϕ0 = [ϕH
+0 , 1]H and ϕ0 = [φ0,1, . . . , φ0,N]T .
+China Communications
+7
+
+Let Hu,k = diag {hu,k,1, . . . , hu,k,N} and Qu,k =
+diag
+�
+|hu,k,1|2 , . . . , |hu,k,N|2 , 1
+�
+. Then, (7) and (19)
+are respectively reformulated as
+P0Tr( ˜
+HrΨ0) + σ2
+vTr(Ψ0) ≤ Pr,
+(27)
+ek ≤ βτ0Tr[(V + σ2
+vQu,k)Ψ0] − βτ0σ2
+v, ∀k, (28)
+where
+V =
+�HH
+u,kHrW0HH
+r Hu,k
+HH
+u,kHrW0hd,k
+hH
+d,kW0HH
+r Hu,k
+hH
+d,kW0hd,k
+�
+,
+and
+˜
+Hr =
+�HrHH
+r
+0
+0
+0
+�
+.
+With the obtained solutions in Sections 4.1 and 4.2,
+P1 can be equivalently written as
+(P2-2) max
+Ψ0,τ,e
+K
+�
+k=1
+τk log
+�
+1 + ǫk
+ek
+τk
+�
+(29)
+s.t.
+Ψ0 ⪰ 0, rank(Ψ0) = 1,
+(30)
+[Ψ0]n,n ≤ a2
+max, ∀n,
+(31)
+[Ψ0]N+1,N+1 = 1,
+(32)
+(1), (20), (22), (27) and (28).
+Similarly, after the relaxation of the rank-one con-
+straint in (30), P2-2 is also an SDP and can be solved
+by the interior-point method. Recall that the tightness
+of optimizing W0 by SDR can be guaranteed, we can
+also prove that the obtained solution Ψ0 is rank-one.
+Then, ˜ϕ0 can be recovered by implementing Cholesky
+decomposition of Ψ0, and the optimal reflection co-
+efficient vector for the WET ϕ∗
+0 can be obtanied by
+linear operation from ˜ϕ0. Subsequently, the optimal
+RIS reflecting coefficient matrix Φ∗
+0 can be obtained
+by Φ∗
+0 = diag((ϕH
+0 )∗).
+Finally, we continue to update the optimal energy
+transmission time τ0 ∈ [0, 1] by the one-dimensional
+search method. Thus, the maximum sum-rate of this
+sub-problem is achieved with the optimal solution
+{Φ∗
+0, τ ∗
+0 , τ ∗, p∗}. The procedure is summarized in Al-
+gorithm 1.
+Algorithm 1. SDP-based RIS reflecting coefficients for the WET
+and resource allocation optimization
+Input: w0, {wk}, {Φk}, ∀k
+Output: Φ∗
+0, τ ∗
+0 , τ ∗, p∗
+1: Initialization: The maximum objective function
+value Rmax = 0 and the step size δ.
+2: for τ0 = 0 : δ : 1 do
+3:
+Given w0, {wk}, {Φk}, we obtain τ ′
+0, Ψ′
+0, τ ′
+k,
+e′
+k, ∀k by solving P2-2.
+4:
+Calculate R = �K
+k=1 τ ′
+k log
+�
+1 + ǫk
+e′
+k
+τ ′
+k
+�
+.
+5:
+if R > Rmax then
+6:
+Update Rmax ← R.
+7:
+Update τ0 ← τ ′
+0, Ψ0 ← Ψ′
+0, τk ← τ ′
+k, ek ←
+e′
+k.
+8:
+end if
+9: end for
+10: Obtain ˜ϕ0 from Ψ0 by Cholesky decomposition.
+11: Obtain ϕ0 from ˜ϕ0.
+12: Set Φ∗
+0 = diag((ϕH
+0 )∗).
+13: Calculate p∗
+k = e∗
+k/τ ∗
+k.
+14: return Φ∗
+0, τ ∗
+0 , τ ∗, p∗.
+4.4 SCA-based RIS Reflecting Coefficients
+Optimization for the WIT
+In this sub-section, we investigate the optimization of
+RIS reflecting coefficient matrix Φk in the WIT phase,
+which is given by
+(P3) max
+Φk
+K
+�
+k=1
+Rk
+(33)
+s.t.
+(9) and (11).
+Note that P3 is still a non-convex optimization prob-
+lem as the active RIS introduces additional noise term
+in the denominator of the objective function, which re-
+sults in a quadratic fractional programming problem.
+In fact, the RIS reflecting coefficients include ampli-
+tude reflection coefficients and phase shifts. To sim-
+plify this problem, we derive the optimal phase shifts
+in the closed-form and then exploit an SCA algorithm
+to obtain the near-optimal amplitude reflection coeffi-
+cients according to [20].
+It is worth noting that P3 can be decomposed into K
+8
+China Communications
+
+independent subproblems, each of which maximizes
+the SNR of Uk at the RS during τk with respect to the
+RIS reflection coefficient vector ϕk. Specifically, with
+w∗
+k obtained in (17) and introducing some new aux-
+iliary variables, the k-th SNR maximization problem
+can be formulated as
+γk = pk
+��bH
+k ϕk + gd,k
+��2
+ϕH
+k Qrϕkσ2v + σ2r
+,
+(34)
+where gd,k
+=
+wH
+k gd,k, gH
+r,k
+=
+wH
+k Gr, bH
+k
+=
+gH
+r,kdiag (gu,k), Qr = diag
+�
+|gr,k,1|2 , . . . , |gr,k,N|2�
+,
+∀k. Let Fk = pkGu,k + σ2
+vIN, ∀k. The subproblem
+can be expressed as
+(P4) max
+ϕk
+γk
+(35)
+s.t.
+ϕH
+k Fkϕk ≤ Pr, ∀k,
+(36)
+(9).
+To solve P4, we decompose the optimization of RIS
+reflecting coefficient vector ϕk into two sub-problems
+for the amplitude reflection coefficient design and the
+optimal phase shift design, respectively. Let ϕk =
+Θk ¯ϕk, where Θk
+=
+diag
+�
+ejθk,1, . . . , ejθk,N�
+∈
+CN×N and ¯ϕk = [ak,1, . . . , ak,N]T ∈ RN×1.
+4.4.1 Optimization of phase shifts for the WIT
+The optimal design of phase shifts is given in the fol-
+lowing proposition.
+Proposition 2. The optimal RIS phase shift of the n-th
+RE for the WIT during τk is derived as
+θ∗
+k,n = arg(gd,k) − arg(gu,k,n) + arg(gr,k,n), (37)
+∀k, ∀n,
+where gu,k,n and gr,k,n denote the n-th element of the
+vector gu,k and gr,k, respectively.
+Proof. Please refer to Appendix B.
+4.4.2 Optimization of amplitude reflection coeffi-
+cients for the WIT
+For P4, the optimal design of phase shifts shown in
+Proposition 2 holds because the value of the ampli-
+fication power in (9) and (36) and the noise power
+in the denominator of (34) are independent with the
+phase shift of each RE. In addition, optimizing θk,n
+is equivalent to maximizing the objective function in
+(34) [20]. With the optimal phase shifts in Proposition
+2, we proceed to optimize the RIS amplitude reflec-
+tion coefficients for the WIT. In particular, P4 can be
+simplified as
+(P4-1) max
+¯ϕk
+¯γk = pk
+��¯bH
+k ¯ϕk + |gd,k|
+��2
+¯ϕH
+k Qr ¯ϕkσ2v + σ2r
+(38)
+s.t.
+¯ϕH
+k Fk ¯ϕk ≤ Pr, ∀k,
+(39)
+ak,n ≤ an,max, ∀k, ∀n,
+(40)
+where ¯γk = |γk|, and ¯bk is element-wise modulus
+of bk. To deal with the non-convexity of the objec-
+tive function (38), we introduce a new auxiliary vari-
+able nk = ¯ϕH
+k Qr ¯ϕkσ2
+v + σ2
+r, which denotes the noise
+power received at the RIS. Then, P4-1 can be con-
+verted into the following equivalent form
+(P4-2) max
+¯γk,nk, ¯ϕk ¯γk
+(41)
+s.t.√pk
+�¯bH
+k ¯ϕk + |gd,k|
+�
+≥ √nk¯γk, ∀k,
+(42)
+¯ϕH
+k Qr ¯ϕkσ2
+v + σ2
+r ≤ nk, ∀k,
+(43)
+(39) and (40).
+However, the constraint (42) is still non-convex. To
+solve P4-1 efficiently, we exploit the SCA algorithm to
+approximate the square root by a convex upper-bound
+in each iteration. Define ¯γk(t) and nk(t) as the iter-
+ative optimization variables after the t-th step itera-
+tion. In terms of {¯γk (t) , nk (t)}, the first-order Tay-
+lor polynomial is used to approximate √nk¯γk, which
+is given by
+√nk¯γk ≤G(¯γk, nk; t)
+=
+�
+¯γk(t)nk(t) + 1
+2
+�nk(t)
+¯γk(t)
+� 1
+2
+[ ¯γk − ¯γk(t)]
++ 1
+2
+� ¯γk(t)
+nk(t)
+� 1
+2
+[n − nk(t)] .
+(44)
+Based on (44), (42) can be rewritten as
+√pk
+�¯bH
+k ¯ϕk + |gd,k|
+�
+≥ G(¯γk, nk; t), ∀k.
+(45)
+China Communications
+9
+
+Then, P4-2 can be reformulated as the following
+problem
+(P4-3) max
+¯γk,nk, ¯ϕk ¯γk,
+(46)
+s.t.(39), (40), (43) and (45).
+As P4-3 is convex and can be solved by the inter-
+point method. We then discuss the initialization of
+¯γk(t) and nk(t). First, we propose an initial solution
+¯ϕk(0) by solving a simple feasible version of problem
+P4-1, i.e., ¯ϕk(0), satisfying the constraints (39) and
+(40). Then, the reasonable initialization of ¯γk(0) and
+nk(0) is given by
+¯γk(0) = pk
+��¯bH
+k ¯ϕk(0) + |gd,k|
+��2
+σ2v ¯ϕH
+k (0)Qr ¯ϕk(0) + σ2r
+,
+(47)
+nk(0) = σ2
+v ¯ϕH
+k (0)Qr ¯ϕk(0) + σ2
+r.
+(48)
+With the initialization described in (47) and (48), the
+optimal amplitude reflection coefficients for the WIT,
+denoted by ¯ϕ∗
+k, can be obtained by iteratively solving
+P4-3 until the convergence is achieved. As a result, the
+RIS reflecting coefficients during τk can be calculated
+by
+Φ∗
+k = diag (Θ∗
+k ¯ϕ∗
+k) , ∀k,
+(49)
+where Θ∗
+k = diag{ejθ∗
+k,1, . . . , ejθ∗
+k,N}.
+The detailed description of optimizing the RIS re-
+flecting coefficients in P3 is summarized in the Algo-
+rithm 2.
+Algorithm 2. SCA-based RIS reflecting coefficients for the WIT
+Input: {wk}, p, ∀k
+Output: {Φ∗
+k}, ∀k
+1: Initialization: ¯γk(t), nk(t), ¯ϕk(t), and t = 0.
+2: Obtain θ∗
+k,n in Proposition 2 and have Θ∗
+k.
+3: repeat
+4:
+t = t + 1.
+5:
+Update ¯γk(t), nk(t), ¯ϕk(t) by solving P4-3.
+6: until the convergence is achieved.
+7: Obtain Φ∗
+k = diag (Θ∗
+k ¯ϕ∗
+k), where ¯ϕ∗
+k = ¯ϕk(t).
+8: return {Φ∗
+k}.
+4.5 Algorithm Summarization and Analysis
+Based on the above analysis, the algorithm for solving
+P1 is summarized in Algorithm 3. Based on the opti-
+mality analysis,the objective function of P1 is a non-
+decreasing function. Due to the power budget con-
+straint (2), (7) and (11), the optimal objective value
+of problem P1 is bounded. Hence, the convergence
+of Algorithm 2 can be thus guaranteed, which will be
+also confirmed by numerical simulations in Section V.
+4.5.1 Complexity Analysis
+The computational complexity of our proposed AO
+algorithm is analyzed as follows, which contains
+the linear MMSE-based receive beamforming cal-
+culation, the SDR algorithm and the SCA algo-
+rithm in each iteration.
+For the linear MMSE-
+based receive beamforming optimization, we derive
+a closed-form solution to the (17), and the approx-
+imate worst-case computational complexity is given
+by O
+�
+KL max(N, L)2�
+.
+According to [36], for
+the subproblem of SDP-based transmit beamform-
+ing optimization, the worst-case computational com-
+plexity is O
+�
+max(K, M)4.5 log(1/ǫ)
+�
+, where ǫ is the
+computational accuracy of the interior-point method
+in CVX. Similarly, for the SDP-based RIS reflect-
+ing coefficients for the WET and resource alloca-
+tion optimization, the worst-case computational com-
+plexity is O
+�
+Iτ max(N, K)4.5 log(1/ǫ)
+�
+, where Iτ
+is the iteration number for updating τ0.
+For the
+SCA-based RIS reflecting coefficients optimization in
+the WIT, the computational complexity is less than
+O
+�
+ISKN 3.5 log(N/ǫ)
+�
+, where IS is the iteration
+number for the SCA algorithm. Thus, the computa-
+tional complexity of the overall AO algorithm is given
+by
+O
+�
+IA
+�
+KL max(N, L)2 + max(K, M)4.5 log(1/ǫ)
++Iτ max(N, K)4.5 log(1/ǫ) + ISKN 3.5 log(N/ǫ)
+��
+,
+(50)
+where IA denotes the number of iterations required for
+convergence.
+4.5.2 Optimality Analysis
+As the formulated problem P1 is extremely non-
+convex, it is very difficult to obtain the globally op-
+timal solution. To solve P1 efficiently, we propose
+10
+China Communications
+
+an efficient AO algorithm to obtain the suboptimal so-
+lutions. Firstly, we obtain the optimal receive beam-
+forming {wk} in a closed-form, which are the globally
+optimal solutions. With the obtained receive beam-
+forming solutions, the formulated problem can be sim-
+plified but is still non-convex.
+Secondly, the SDR
+technique is adopted to optimize the transmit beam-
+forming, the RIS reflecting coefficient matrices for
+the WET phase, the transmit power at each user, and
+the network time scheduling. In particular, we prove
+the obtained solutions of P2-1 and P2-2 are rank-one.
+Since the tightness of applying SDR can be guaran-
+teed, the obtained solutions {w0, Φ0, τ, p} are glob-
+ally optimal [23]. Then, we use the one-dimensional
+search method to exploit the optimal energy trans-
+mission time τ0 by setting an appropriate step size.
+Thirdly, for the optimization of RIS reflecting coef-
+ficients for the WIT phase, we decompose P4 into two
+sub-problems. On the one hand, the optimal phase
+shifts have been derived in a closed-form which has
+been proved. On the other hand, P4-1 is solved by
+Algorithm 2, which obtains the reflection amplitudes
+of {Φk} are near-optima of the original problem [38].
+Hence, Algorithm 3 can be used to obtain the near-
+optimal solutions to P1 with a high accuracy.
+Algorithm 3. AO algorithm for P1
+1: Initialization: w0, {wk}, Φ0, {Φk}, τ0, τ, p, ∀k.
+2: repeat
+3:
+Given Φk and p, update {wk} by (17).
+4:
+Given Φ0, τ0, {Φk}, {wk}, update w0 with by
+solving P2-1.
+5:
+Given w0, {wk}, {Φk}, update Φ0, τ0, τ and p
+by Algorithm 1.
+6:
+Given {wk} and p, update {Φk} by Algorithm
+2.
+7: until �K
+k=1 Rk converged.
+8: return w∗
+0, {w∗
+k}, Φ∗
+0, {Φ∗
+k}, τ ∗
+0 , τ ∗, p∗.
+V. NUMERICAL RESULTS
+In this section, numerical results are presented to eval-
+uate the performance of the proposed scheme.
+As
+shown in Figure 3, we consider that the simulated net-
+work deployment is a 2-D coordinate system, where
+���
+��
+ (!)
+(0,0)
+( ", 0)
+( #, 0)
+$(!)
+( %,  &)
+���������
+��
+Figure 3. Placement model of simulation setup.
+the coordinates of the PS, the RIS, and the RS are
+given as (0,0), (xr, 0), and (xs,0), respectively, the
+users are randomly deployed within a circular area
+centered at (xu, xh) with radius 1m. We follow the
+channel model considered in [29]. In particular, the
+large-scale path-loss is modeled as L = A(d/d0)−α,
+where A is the path-loss at the reference distance
+d0 = 1m and set as A = −30dB, d denotes the dis-
+tance between two nodes, and α is the path-loss expo-
+nent. For the RIS related links, the path-loss exponent
+is set as 2.2 since the location of RIS can be carefully
+designed to avoid the severe signal blockage. While
+the path-loss exponents for the RIS unrelated links are
+set as 3.5 due to the users’ random deployment. We
+assume the direct link channels follow Rayleigh fad-
+ing but the RIS related channels follow Rician fading.
+Specifically, the small-scale channel from the PS to the
+RIS can be expressed as
+Hr =
+��
+βr
+βr + 1
+¯
+HLoS
+r
++
+�
+1
+βr + 1
+¯
+HNLoS
+r
+�
+(51)
+where βr is the Rician factor for the PS-RIS link,
+¯
+HLoS
+r
+denotes the deterministic line of sight (LoS)
+component, and ¯
+HNLoS
+r
+denotes the non-LoS compo-
+tent with circularly symmetric complex Gaussian ran-
+dom variables with zero mean and unit variance. The
+other channels can be similarly defined. Unless oth-
+erwise stated, other parameters are given as follows:
+βr = 10 [39], ρ = 0.8, σ2
+v = σ2
+r = −90dBm,
+P0 = 20dBm [20], Pr = 20dBm, amax = 25dB
+[40], N = 10, K = 4, M = 4, L = 4, xr = 10m,
+xu = 10m, xs = 20m, and xh = 2m.
+For comparisons, we also evaluate the performance
+of the following benchmark schemes:
+(1) Active RIS-aided single-antenna WPCN scheme
+(Active-SA).
+China Communications
+11
+
+(2) Passive RIS-aided multi-antenna WPCN scheme
+(Passive-MA).
+(3) Active RIS-aided multi-antenna WPCN with uni-
+form energy beamforming scheme (Active-MA-
+UEBF).
+Notice that for the multi-antenna schemes, the num-
+ber of antennas is set as 4 in the PS and RS. In addition,
+we set the number of REs in the Passive-MA scheme
+as N = 100 to show the superiority of the proposed
+scheme.
+Before performance comparisons, we first show the
+convergence performance of the proposed AO algo-
+rithm in Figure 4. One can observe that as the num-
+ber of iterations increases, the sum-rate first increases
+but finally converges to a constant after nearly 8 iter-
+ations. This demonstrates that the convergence of the
+proposed scheme can be achieved quickly. The other
+observation is that the effect of the parameter setting
+on convergence is limited.
+2
+4
+6
+8
+10
+12
+Number of iterations
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+Sum rate (bps/Hz)
+N=10, M=L=4
+N=10, M=L=8
+N=20, M=L=4
+N=20, M=L=8
+N=30, M=L=4
+N=30, M=L=8
+Figure 4.
+Convergence behavior of the proposed scheme
+under different parameter settings.
+Figure 5 shows the impact of the transmit power
+at the PS (i.e., P0) on the sum-rate when the RIS’s
+maximum reflecting power Pr = 10, 20 dBm and
+the RIS’s maximum amplitude reflection coefficient
+amax = 10, 25 dB, respectively. In general, the pro-
+posed scheme outperforms the Active-SA scheme with
+the same parameters, which confirms that the assis-
+tance of multiple antennas can achieve a significant
+performance gain by constructing the transmit beam-
+forming at the PS and the receive beamforming at the
+RS. For a given amax = 25 dB, our proposed scheme
+with 10 REs can achieve 415.48% performance gain
+5
+10
+15
+20
+25
+30
+35
+40
+45
+Transmit power at the PS(dBm)
+0
+5
+10
+15
+20
+25
+30
+35
+Sum rate (bps/Hz)
+Proposed, Pr=20, amax=25
+Proposed, Pr=20, amax=10
+Proposed, Pr=10, amax=25
+Proposed, Pr=10, amax=10
+Active-SA, Pr=20, amax=25
+Active-SA, Pr=20, amax=10
+Passive-MA, N=100
+Figure 5. Sum-rate versus the transmit power at the PS.
+compared to the passive RIS scheme with 100 REs
+when P0 = 20 dBm. Indeed, the active RIS can con-
+siderably make use of its amplification characteristic
+to amplify the energy signals at low transmit power
+and thereby realize a superior capability at the cost of
+additional power consumption. For a given amax = 10
+dB, it can be seen that the sum-rates achieved by the
+proposed scheme with Pr = 20 dBm and Pr = 10
+dBm are almost the same, which implies that the am-
+plification power constraints defined in (7) and (11)
+are inactive since amax is limited for the small trans-
+mit power. Note that, the performance gap is signif-
+icant between the scheme with amax = 25 dB and
+amax = 10 dB because amax directly limits the ampli-
+tude reflection coefficient of the active RIS. In addi-
+tion, the sum-rate of the passive-MA scheme is gener-
+ally lower than the active RIS schemes with the same
+REs and the passive RIS needs to be equipped with
+more REs (e.g., 100 REs) to achieve the similar per-
+formance.
+In Figure 6, we evaluate the sum-rate versus the
+number of reflecting elements at the RIS. It can be
+seen that the proposed schemes can achieve a higher
+performance gain compared with the other benchmark
+schemes. With an increasing number of reflecting ele-
+ments, the sum-rate increases due to the fact that more
+transmission links can be provided for both the WET
+and the WIT. In addition, to investigate the best system
+performance, the maximum number of users is set to
+be equal to the number of REs. Since the active RIS
+can amplify the incident signals, a limited number of
+REs is sufficient to reach the desired SNR. Therefore,
+the size of active RIS can be reduced, making it ap-
+12
+China Communications
+
+5
+10
+15
+20
+25
+30
+35
+Number of REs
+10
+12
+14
+16
+18
+20
+22
+24
+Sum rate (bps/Hz)
+Proposed, K=4
+Proposed, K=N
+Active-SA, K=4
+Active-SA, K=N
+Active-MA-UEBF, K=4
+Active-MA-UEBF, K=N
+Figure 6. Sum-rate versus number of reflecting elements at
+the RIS.
+2
+3
+4
+5
+6
+7
+8
+9
+10
+Number of Users
+2
+4
+6
+8
+10
+12
+14
+16
+18
+20
+Sum rate (bps/Hz)
+Proposed
+Active-SA
+Active-MA-UEBF
+Passive-MA
+Figure 7. Sum-rate versus the number of users.
+plicable to the scenario where the space for the RIS
+deployment is limited.
+In Figure 7, we study the effect of number of user
+on the sum-rate. As the number of users increases,
+the total amount of harvested energy by users im-
+proves, which results in a higher sum-rate. Nonethe-
+less, when the number of users reaches a threshold,
+e.g.
+K = 8, the sum-rate achieved by our pro-
+posed scheme becomes to be saturated. This is due
+to the fact that the increment of number of users re-
+duces the energy transfer duration and the time allo-
+cated to each user for information transmission, which
+makes the sum-rate converge to a constant. Again,
+our proposed scheme notably outperforms the other
+benchmark schemes.
+For example, when the num-
+ber of users is K = 4, our proposed scheme can
+achieve 17.78% and 415.48% performance gain com-
+1
+2.5
+4
+5.5
+7
+8.5
+10
+11.5
+13
+14.5
+16
+17.5
+19
+Location of RIS
+0
+5
+10
+15
+20
+25
+Sum rate (bps/Hz)
+Proposed
+Active-SA
+Active-MA-UEBF
+Passive-MA
+Figure 8. Sum-rate versus x-coordinate of the RIS.
+pared with the Active-SA scheme and the Passive-MA
+scheme with 100 REs, respectively.
+In Figure 8, we plot the sum-rate versus the hori-
+zontal ordinate of the RIS. As xr varies, the sum-rates
+of all schemes first increase but then decrease. Com-
+pared to the scenario that the RIS is close to the RS,
+by deploying the RIS near the PS, e.g., xr = 1, the
+sum-rate can be improved.
+It is because the users
+can harvest more energy assisted by the active RIS.
+Moreover, we can observe that the sum-rate is maxi-
+mized at xr = 10, where the reflecting link between
+the active RIS and each user is strongest so the users
+can benefit from a larger amplification and reflection
+gain. However, when the RIS is neither close to the
+PS nor the users, both the PS-RIS link and the RIS-
+users links become weak, which results in the reduce
+of harvested energy. Furthermore, since the Active-
+MA-UEBF scheme adopts the uniform energy beam-
+forming, the energy signals cannot adaptively align
+with the direction of the desired channels, which re-
+sults in a low WET efficiency. In addition, the schemes
+with the active RIS can achieve a much better perfor-
+mance than the passive RIS scheme, which demon-
+strates that the active RIS with the amplification func-
+tionality can significantly mitigates the double-fading
+effect. The above observation demonstrates that the lo-
+cation of the active RIS should be carefully designed.
+VI. CONCLUSIONS
+In this paper, we have proposed an active RIS as-
+sisted relaying scheme to enhance the performance
+of multiuser multi-antenna WPCN, which is involved
+China Communications
+13
+
+in both the WET from the PS to users and the WIT
+from users to the RS. To further enhance system per-
+formance, both transmit beamforming at the PS and
+receive beamforming at the RS have been designed.
+We have formulated a system sum-rate maximization
+problem by jointly optimizing the RIS reflection coef-
+ficients for both the WET and the WIT, transmit and
+receive beamforming vectors, transmit power at each
+user, and network time scheduling. As the formulated
+problem is non-convex, we have proposed an AO al-
+gorithm with linear MMSE, SDR and SCA techniques
+to solve it efficiently. Finally, numerical results have
+been provided to confirm the performance superiority
+of the proposed scheme.
+APPENDIX
+A. Proof of Proposition 1
+The Lagrangian function of P2-1 can be expressed as
+L =
+K
+�
+k=1
+λkβTr(Hd,kW0) − ξTr(W0)
++ Tr(ΩW) + δ, ∀k,
+(52)
+where λk ≥ 0, ξ ≥ 0, and Ω ∈ HM are the Lagrange
+multipliers associated with constraints (21), (22), and
+(24), respectively, δ denotes the term unrelated with
+W0. The Karush-Kuhn-Tucker (KKT) conditions of
+P2-1 are given as follows
+∂L
+∂W0
+=
+K
+�
+k=1
+λ∗
+kβHd,k − ξ∗IM + Ω∗ = 0,
+(53)
+Ω∗W ∗
+0 = 0,
+(54)
+where λ∗
+k, ξ∗ and Ω∗ are the optimal Lagrangian mul-
+tipliers for the dual problem of P2-1. It can be proved
+that λ∗
+k > 0 and ξ∗ > 0 since the constraints (21) and
+(22)are equalities in the optimal condition. Based on
+(53) and (54), it is straightforward to obtain the fol-
+lowing equality
+(ξ∗IM −
+K
+�
+k=1
+λ∗
+kβHd,k)W ∗
+0 = 0
+(55)
+According to [41], rank(ξ∗IM −�K
+k=1 λ∗
+kβHd,k) ≥
+M − 1 due to the fact that Hd,k for ∀k are indepen-
+dently distributed. Thus, from (55), we can obtain that
+rank(W0) ≤ 1. It is obvious that W0 = 0 is not
+the optimal solution to P2-1. Hence, we derive that
+rank(W0) = 1, which thus proves Proposition 1.
+B. Proof of Proposition 2
+Since Qr and Fk are diagonal matrices, we observe
+that the noise power in the denominator of (35) and the
+amplification power in (9) and (36) are independent
+of the phase shift of each RE. Therefore, maximizing
+γk with respect to Θk is equivalent to the following
+optimization problem
+(P4-4) max
+Θk
+��bH
+k Θk ¯ϕk + gd,k
+��2
+(56)
+s.t.
+|Θk,n| = 1, ∀k, ∀n.
+(57)
+We rewrite the objective function as
+��bH
+k Θk ¯ϕk
+��2 + |gd,k|2 + 2
+��bH
+k Θk ¯ϕk
+�� |gd,k| cos α,
+(58)
+where α = arctan Im(bH
+k Θk ¯ϕk)
+Re(bH
+k Θk ¯ϕk) − arctan Im(gd,k)
+Re(gd,k).
+Obviously, the maximum of
+��bH
+k Θk ¯ϕk + gd,k
+��2 is
+achieved when arg(bH
+k Θk ¯ϕk) = arg(gd,k) ≜ ω.
+Let vk = [vk,1, vk,2, ..., vk,N]T ∈ RN×1 and ξk =
+diag(bH
+k ) ¯ϕk.
+As bH
+k Θk ¯ϕk = vH
+k ξk, P4-4 can be
+rewritten as
+(P4-5) max
+vk
+��vH
+k ξk
+��2
+(59)
+s.t.
+|vk,n| = 1, ∀k, ∀n,
+(60)
+arg(vH
+k ξk) = ω, ∀k.
+(61)
+Based on [12],
+the optimal solution to P4-
+5 can be expressed as v∗
+k
+=
+ej(ω−arg(ξk))
+=
+ej(ω−arg(diag(bH
+k ) ¯ϕk)).
+Then, the optimal RIS phase
+shift for the n-th RE is expressed as θk,n
+=
+arg(gd,k) − arg(bH
+k,n) − arg( ¯ϕk,n). Finally, we ob-
+tain that θk,n = arg(gd,k)−arg(gu,k,n)+arg(gr,k,n),
+∀k, ∀n. This completes the proof of Proposition 2.
+References
+[1] SOMOV A, GIAFFREDA R. Powering IoT de-
+vices: Technologies and opportunities[J]. IEEE
+IoT Newsletter, 2015.
+[2] VARSHNEY L R. Transporting information and
+energy simultaneously[C]//2008 IEEE Interna-
+14
+China Communications
+
+tional Symposium on Information Theory. IEEE,
+2008: 1612-1616.
+[3] ZHONG C, SURAWEERA H A, ZHENG G,
+et al. Wireless information and power transfer
+with full duplex relaying[J]. IEEE Transactions
+on Communications, 2014, 62(10): 3447-3461.
+[4] WU Q, GUAN X, ZHANG R. Intelligent reflect-
+ing surface-aided wireless energy and informa-
+tion transmission: An overview[J]. Proceedings
+of the IEEE, 2021.
+[5] ZHANG R, HO C K.
+MIMO broadcasting
+for simultaneous wireless information and power
+transfer[J]. IEEE Transactions on Wireless Com-
+munications, 2013, 12(5): 1989-2001.
+[6] JU H, ZHANG R.
+Throughput maximization
+in wireless powered communication networks
+[J]. IEEE Transactions on Wireless Communi-
+cations, 2013, 13(1): 418-428.
+[7] JU H, ZHANG R.
+User cooperation in
+wireless powered communication networks[C]//
+2014 IEEE Global Communications Conference.
+IEEE, 2014: 1430-1435.
+[8] JU H, ZHANG R. Optimal resource allocation
+in full-duplex wireless-powered communication
+network[J]. IEEE Transactions on Communica-
+tions, 2014, 62(10): 3528-3540.
+[9] KIM J, LEE H, SONG C, et al. Sum through-
+put maximization for multi-user MIMO cogni-
+tive wireless powered communication networks
+[J]. IEEE Transactions on Wireless Communica-
+tions, 2016, 16(2): 913-923.
+[10] WU Q, TAO M, NG D W K, et al.
+Energy-
+efficient resource allocation for wireless pow-
+ered communication networks[J]. IEEE Trans-
+actions on Wireless Communications, 2015, 15
+(3): 2312-2327.
+[11] WU Q, CHEN W, LI J. Wireless powered com-
+munications with initial energy: QoS guaranteed
+energy-efficient resource allocation[J].
+IEEE
+Communications Letters, 2015, 19(12): 2278-
+2281.
+[12] WU Q, ZHANG R. Intelligent Reflecting Sur-
+face Enhanced Wireless Network via Joint Ac-
+tive and Passive Beamforming[J]. IEEE Trans-
+actions on Wireless Communications, 2019, 18
+(11): 5394-5409.
+[13] DI RENZO M, ZAPPONE A, DEBBAH M, et al.
+Smart radio environments empowered by recon-
+figurable intelligent surfaces: How it works, state
+of research, and the road ahead[J]. IEEE journal
+on selected areas in communications, 2020, 38
+(11): 2450-2525.
+[14] KUNDU N K, MCKAY M R.
+RIS-Assisted
+MISO Communication:
+Optimal Beamform-
+ers and Performance Analysis[C]//2020 IEEE
+Globecom Workshops (GC Wkshps. Taipei, Tai-
+wan: IEEE, 2020: 1-6.
+[15] ZOU Y, GONG S, XU J, et al. Wireless pow-
+ered intelligent reflecting surfaces for enhancing
+wireless communications[J]. IEEE Transactions
+on Vehicular Technology, 2020, 69(10): 12369-
+12373.
+[16] ZHANG Z, DAI L. A joint precoding framework
+for wideband reconfigurable intelligent surface-
+aided cell-free network[J]. IEEE Transactions on
+Signal Processing, 2021, 69: 4085-4101.
+[17] LIANG Y C, CHEN J, LONG R, et al. Recon-
+figurable intelligent surfaces for smart wireless
+environments: Channel estimation, system de-
+sign and applications in 6G networks[J]. Science
+China Information Sciences, 2021, 64(10): 1-21.
+[18] YU X, JAMALI V, XU D, et al. Smart and recon-
+figurable wireless communications: From IRS
+modeling to algorithm design[J]. IEEE Wireless
+Communications, 2021, 28(6): 118-125.
+[19] ZHANG Z, DAI L, CHEN X, et al. Active RIS
+vs. passive RIS: Which will prevail in 6G?[A].
+2021. arXiv: 2103.15154.
+[20] LONG R, LIANG Y C, PEI Y, et al.
+Active
+reconfigurable intelligent surface-aided wireless
+communications[J]. IEEE Transactions on Wire-
+less Communications, 2021, 20(8): 4962-4975.
+[21] LYU B, RAMEZANI P, HOANG D T, et al.
+Optimized Energy and Information Relaying
+in Self-Sustainable IRS-Empowered WPCN[J].
+IEEE TRANSACTIONS ON COMMUNICA-
+TIONS, 2021, 69(1): 15.
+[22] ZHENG Y, BI S, ZHANG Y J A, et al. Joint
+beamforming and power control for throughput
+maximization in IRS-assisted MISO WPCNs[J].
+IEEE Internet of Things Journal, 2021, 8(10):
+8399-8410.
+[23] HUA M, WU Q, POOR H V. Power-Efficient
+Passive Beamforming and Resource Allocation
+for IRS-Aided WPCNs[J]. IEEE Transactions on
+Communications, 2022.
+China Communications
+15
+
+[24] XU Y, GAO Z, WANG Z, et al. RIS-enhanced
+WPCNs: Joint radio resource allocation and pas-
+sive beamforming optimization[J]. IEEE Trans-
+actions on Vehicular Technology, 2021, 70(8):
+7980-7991.
+[25] YOU C, ZHANG R. Wireless communication
+aided by intelligent reflecting surface: Active
+or passive?[J]. IEEE Wireless Communications
+Letters, 2021, 10(12): 2659-2663.
+[26] DONG L, WANG H M, BAI J.
+Active Re-
+configurable Intelligent Surface Aided Secure
+Transmission[J]. IEEE Transactions on Vehic-
+ular Technology, 2021.
+[27] ZARGARI S, HAKIMI A, TELLAMBURA C,
+et al. Multiuser MISO PS-SWIPT Systems: Ac-
+tive or Passive RIS?[J]. IEEE Wireless Commu-
+nications Letters, 2022.
+[28] GAO Y, WU Q, ZHANG G, et al. Beamform-
+ing Optimization for Active Intelligent Reflect-
+ing Surface-Aided SWIPT[A].
+2022.
+arXiv:
+2203.16093.
+[29] ZENG P, QIAO D, WU Q, et al.
+Throughput
+Maximization for Active Intelligent Reflecting
+Surface Aided Wireless Powered Communica-
+tions[J].
+IEEE Wireless Communications Let-
+ters, 2022.
+[30] WU Q, ZHANG R. Weighted Sum Power Maxi-
+mization for Intelligent Reflecting Surface Aided
+SWIPT[J]. IEEE WIRELESS COMMUNICA-
+TIONS LETTERS, 2020, 9(5): 5.
+[31] HU S, WEI Z, CAI Y, et al.
+Robust and se-
+cure sum-rate maximization for multiuser MISO
+downlink systems with self-sustainable IRS[J].
+IEEE Transactions on Communications, 2021,
+69(10): 7032-7049.
+[32] ZHENG B, ZHANG R.
+Intelligent reflect-
+ing surface-enhanced OFDM: Channel estima-
+tion and reflection optimization[J]. IEEE Wire-
+less Communications Letters, 2019, 9(4): 518-
+522.
+[33] WU Q, ZHANG S, ZHENG B, et al.
+Intel-
+ligent reflecting surface-aided wireless commu-
+nications: A tutorial[J]. IEEE Transactions on
+Communications, 2021, 69(5): 3313-3351.
+[34] WANG Z, LIU L, CUI S.
+Channel Estima-
+tion for Intelligent Reflecting Surface Assisted
+Multiuser Communications: Framework, Algo-
+rithms, and Analysis[J]. IEEE Transactions on
+Wireless Communications, 2020, 19(10): 6607-
+6620.
+[35] ZHENG Y, BI S, ZHANG Y J, et al.
+Intel-
+ligent reflecting surface enhanced user cooper-
+ation in wireless powered communication net-
+works[J]. IEEE Wireless Communications Let-
+ters, 2020, 9(6): 901-905.
+[36] LUO Z Q, MA W K, SO A, et al. Semidefinite
+Relaxation of Quadratic Optimization Problems
+[J]. IEEE Signal Processing Magazine, 2010, 27
+(3): 20-34.
+[37] BOYD S, BOYD S P, VANDENBERGHE L.
+Convex optimization[M]. Cambridge university
+press, 2004.
+[38] RAZAVIYAYN M. Successive Convex Approx-
+imation: Analysis and Applications[D]. Univer-
+sity of Minnesota, 2014.
+[39] GUO H, LIANG Y C, CHEN J, et al. Weighted
+Sum-Rate Maximization for Reconfigurable In-
+telligent Surface Aided Wireless Networks[J].
+IEEE Transactions on Wireless Communica-
+tions, 2020, 19(5): 3064-3076.
+[40] AMATO F, PETERSON C W, DEGNAN B P,
+et al. Tunneling RFID tags for long-range and
+low-power microwave applications[J].
+IEEE
+Journal of Radio Frequency Identification, 2018,
+2(2): 93-103.
+[41] XU X, LIANG Y C, YANG G, et al.
+Recon-
+figurable intelligent surface empowered symbi-
+otic radio over broadcasting signals[J].
+IEEE
+Transactions on Communications, 2021, 69(10):
+7003-7016.
+16
+China Communications
+

2tAzT4oBgHgl3EQffPw3/content/2301.01448v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:52e3119012d28abcb3e31e3a4c4d7e3c4ce978b7eca9465e40953ebdeae5f93c
+size 2705653

2tAzT4oBgHgl3EQffPw3/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d2e0733b8a2cae6fef03ecad865e1bb553559562789b707c812a45b8511caeba
+size 262850

39AyT4oBgHgl3EQfo_il/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a9e9abf03196fda13fc079c01130ca85a966551d2fb0c027572d70be6b148f08
+size 3670061

49FKT4oBgHgl3EQfSC3u/content/tmp_files/2301.11774v1.pdf.txt

@@ -0,0 +1,1133 @@
+Reinforcement Learning from Diverse Human Preferences
+Wanqi Xue * 1 Bo An 1 Shuicheng Yan 2 Zhongwen Xu 2
+Abstract
+The complexity of designing reward functions
+has been a major obstacle to the wide application
+of deep reinforcement learning (RL) techniques.
+Describing an agent’s desired behaviors and prop-
+erties can be difficult, even for experts. A new
+paradigm called reinforcement learning from hu-
+man preferences (or preference-based RL) has
+emerged as a promising solution, in which reward
+functions are learned from human preference la-
+bels among behavior trajectories. However, ex-
+isting methods for preference-based RL are lim-
+ited by the need for accurate oracle preference
+labels. This paper addresses this limitation by de-
+veloping a method for crowd-sourcing preference
+labels and learning from diverse human prefer-
+ences. The key idea is to stabilize reward learning
+through regularization and correction in a latent
+space. To ensure temporal consistency, a strong
+constraint is imposed on the reward model that
+forces its latent space to be close to the prior distri-
+bution. Additionally, a confidence-based reward
+model ensembling method is designed to generate
+more stable and reliable predictions. The pro-
+posed method is tested on a variety of tasks in
+DMcontrol and Meta-world and has shown con-
+sistent and significant improvements over existing
+preference-based RL algorithms when learning
+from diverse feedback, paving the way for real-
+world applications of RL methods.
+1. Introduction
+Recent advances in reinforcement learning (RL) have
+achieved remarkable success in simulated environments
+such as board games (Silver et al., 2016; 2018; Moravˇc´ık
+et al., 2017) and video games (Mnih et al., 2015; Vinyals
+et al., 2019; Wurman et al., 2022). However, the application
+*This work was done during an internship at Sea AI
+Lab, Singapore 1Nanyang Technological University, Singapore
+2Sea AI Lab, Singapore.
+Correspondence to:
+Wanqi Xue
+<[email protected]>, Zhongwen Xu <[email protected]>.
+Preprint.
+of RL to real-world problems remains a challenge due to
+the lack of a suitable reward function (Leike et al., 2018).
+On the one hand, designing a reward function to provide
+dense and instructive learning signals is difficult in complex
+real-world tasks (Christiano et al., 2017; Lee et al., 2021b).
+On the other hand, RL agents are likely to exploit a reward
+function by achieving high return in an unexpected and un-
+intended manner (Leike et al., 2018; Ouyang et al., 2022).
+To alleviate the problems, preference-based RL is proposed
+to convey human-preferred objectives to agents (Christiano
+et al., 2017; Stiennon et al., 2020), in which a (human)
+teacher is requested to provide his/her preferences over pairs
+of agents’ historical trajectories. Based on human feedback,
+a reward model is learned and applied to provide learning
+signals to agents (see Fig. 1(a)). Preference-based RL pro-
+vides an effective way to learn from human intentions, rather
+than explicitly designed rewards, and has demonstrated its
+effectiveness in areas such as robotics control (Lee et al.,
+2021b) and dialogue systems (Ouyang et al., 2022).
+Though promising, the learning of preference-based RL
+heavily relies on plenty of expert feedback, which could
+be prohibitively expensive. Existing works typically focus
+on feedback-efficient algorithms. They investigate several
+sampling and exploration strategies with the aim of finding
+the most deserving queries to be labelled (Biyik & Sadigh,
+2018; Lee et al., 2021a; Liang et al., 2022). Some other
+works improve feedback efficiency by learning good policy
+initialization with imitation learning (Ibarz et al., 2018) and
+unsupervised pre-training (Lee et al., 2021b). In addition,
+semi-supervised reward learning is also used for better effi-
+ciency (Park et al., 2022). Although these methods reduce
+the demand for human feedback, scaling preference-based
+RL to large-scale real-world problems is still difficult be-
+cause the need for feedback increases significantly with the
+complexity of problems.
+Recently, there has been a trend to replace expensive expert
+feedback with crowd-sourced data for scalability (Gerst-
+grasser et al., 2022; Ouyang et al., 2022). For example,
+in ChatGPT, a group of annotators are hired for providing
+affordable human feedback to RL agents. The impressive
+results show that preference-based RL has great potential
+when sufficient human feedback is provided. Obtaining hu-
+man feedback from various sources can effectively address
+the issue of data scarcity in preference-based RL. However,
+arXiv:2301.11774v1  [cs.LG]  27 Jan 2023
+
+Reinforcement Learning from Diverse Human Preferences
+Annotation
+Reward learning
+Encoder
+Decoder
+(a)
+(b)
+Figure 1. Illustration of our method. (a) There is a team of different annotators with bounded rationality to provide their preferences.
+Based on the preference data, a reward model is learned and used to provide rewards to an RL agent for policy optimization. (b) The
+reward models encode an input into a latent space where a strong distribution constraint is applied to address inconsistency issues.
+Following that, a novel reward model ensembling method is applied to the decoders to aggregate their predictions.
+this approach also brings some challenges, as the collected
+preferences may be unreliable, inconsistent, or even adver-
+sarial, making it difficult to optimize the policy. The diverse
+nature of the feedback can make it challenging to deter-
+mine the true underlying preferences and to learn from them
+effectively.
+In this paper, we propose a simple yet effective method to
+help existing preference-based RL algorithms learn from
+diverse human preferences. The key idea is to stabilize the
+reward learning by regularizing and correcting its predic-
+tions in a latent space. Concretely, we first map the inputs
+of the reward model to a latent space, enabling the predicted
+rewards to be easily manipulated by varying them in this
+space. Second, to ensure temporal consistency throughout
+the learning process, we impose a strong constraint on the
+latent space by forcing it to be close to a prior distribution.
+This prior distribution serves as a reference point, providing
+a way to measure the consistency of the predicted rewards
+over time. Lastly, we measure the confidence of the re-
+ward model in its predictions by calculating the divergence
+between its latent space and the prior distribution. Based
+on this divergence, we design a confidence-based reward
+model ensembling method to generate more stable and reli-
+able predictions. We demonstrate the effectiveness of our
+method on a variety of complex locomotion and robotic
+manipulation tasks from DeepMind Control Suite (DM-
+Control) (Tassa et al., 2018; Tunyasuvunakool et al., 2020)
+and Meta-world (Yu et al., 2020). The results show that
+our method is able to effectively recover the performance
+of existing preference-based RL algorithms under diverse
+preferences in all the tasks.
+2. Preliminaries
+We consider the reinforcement learning (RL) framework
+which is defined as a Markov Decision Process (MDP). For-
+mally, an MDP is defined by a tuple ⟨S, A, r, P, γ⟩, where
+S and A denote the state and action space, r(s, a) is the
+reward function, P(s′|s, a) denotes the transition dynam-
+ics, and γ ∈ [0, 1) is the discount factor. At each timestep
+t, the agent receives the current state st ∈ S from the
+environment and makes an action at ∈ A based on its
+policy π(at|st). Subsequently, the environment returns a
+reward rt and the next state st+1 to the agent. RL seeks
+to learn a policy such that the expected cumulative return,
+E
+��∞
+k=0 γkr(st+k, at+k)
+�
+, is maximized.
+In realistic applications, designing the reward function to
+capture human intent is rather difficult. Preference-based
+RL is therefore proposed to address this issue by learning
+a reward function from human preferences (Akrour et al.,
+2011; Wilson et al., 2012; Christiano et al., 2017; Ibarz
+et al., 2018). Specifically, there is a human teacher indi-
+cating his/her preferences over pairs of segments (σ0, σ1),
+where a segment is a part of the trajectory of length H, i.e.,
+σ = {(s1, a1), . . . , (sH, aH)}. The preferences y could
+be (0, 1), (1, 0) and (0.5, 0.5), where (0, 1) indicates σ1 is
+preferred to σ0, i.e., σ1 ≻ σ0; (1, 0) indicates σ0 ≻ σ1;
+and (0.5, 0.5) implies an equally preferable case. Each feed-
+back is stored as a triple (σ0, σ1, y) in a preference buffer
+Dp = {((σ0, σ1, y))i}N
+i=1.
+To learn a reward function ˆr from the labeled preferences,
+similar to most prior work (Ibarz et al., 2018; Lee et al.,
+2021b;a; Liang et al., 2022; Park et al., 2022; Hejna III &
+Sadigh, 2022), we define a preference predictor by following
+
+(s, a, r(s, a), s')(s, a, s')AReinforcement Learning from Diverse Human Preferences
+the Bradley-Terry model (Bradley & Terry, 1952):
+Pψ
+�
+σ1 ≻ σ0�
+=
+exp
+��H
+t=1 ˆr
+�
+s1
+t, a1
+t; ψ
+��
+�
+i∈{0,1} exp
+��H
+t=1 ˆr
+�
+si
+t, ai
+t; ψ
+��.
+(1)
+Given the preference buffer Dp, we can train the reward
+function ˆr by minimizing the cross-entropy loss between the
+preference predictor and the actually labeled preferences:
+Ls = −
+E
+(σ0,σ1,y)∼Dp
+�
+y(0) log Pψ
+�
+σ0 ≻ σ1�
++ y(1) log Pψ
+�
+σ1 ≻ σ0��
+.
+(2)
+where y(0) and y(1) are the first and second element of y,
+respectively. With the learned rewards, we can optimize a
+policy π using any RL algorithm to maximize the expected
+return (Christiano et al., 2017).
+3. Preference-based Reinforcement Learning
+from Diverse Human Feedback
+Preference-based RL provides an effective framework to
+deliver human intentions to RL agents. In this section, we
+present our algorithm which helps RL agents to learn from
+human preferences that possess high diversity and incon-
+sistency. The key idea of our algorithm is to stabilize the
+reward learning by regularizing and correcting it in a latent
+space. Specifically, we first map the input of the reward
+model to a latent space so that the predicted reward can
+be easily manipulated by modifying it in the latent space.
+Second, to achieve temporal consistency throughout the
+learning process, we impose a strong constraint on the latent
+space by forcing it to be close to a prior distribution. Last,
+we measure the confidence of a reward model in its predic-
+tion by calculating the divergence between its latent space
+and the prior distribution. Based on the divergence, we de-
+sign a confidence-based reward model ensembling method
+to generate more reliable and stable predictions. The overall
+framework of our algorithm is presented in Figure 1.
+3.1. Manipulating Rewards within a Latent Space
+Reward learning is a key problem in preference-based RL
+because RL agents rely on the guidance of the learned re-
+ward model for policy optimization (Silver et al., 2021).
+However, learning an instructive and stable reward model
+is rather difficult when human preferences possess high
+diversity. If we simply minimize the loss in Eq. 2, the
+generated rewards will have severe fluctuations and incon-
+sistencies because the supervised signal, i.e., the collected
+preferences (y), can be noisy, self-contradictory, or even
+adversarial. As a result, RL agents cannot converge to a rea-
+sonable policy since the learning objectives always change.
+Algorithm 1 RL from Diverse Human Preferences
+1: Input: Strength of constraint φ, number of reward mod-
+els N, frequency of feedback session K
+2: Initialize parameters of policy π(s, a) and the reward
+model ˆr(s, a; ψ)
+3: Initialize preferences buffer Dp ← ∅ and replay buffer
+Dr ← ∅
+4: for each iteration do
+5:
+if iteration % K == 0 then
+6:
+Sample (σ0, σ1) and query annotators for y
+7:
+Store preference Dp ← Dp ∪ {(σ0, σ1, y)}
+8:
+for each reward model updating step do
+9:
+Sample a minibatch of preferences (σ0, σ1, y)
+10:
+Optimize the reward model (Eq. 7)
+11:
+end for
+12:
+end if
+13:
+for each timestep do
+14:
+Collect s′ by taking action a ∼ π(s, a)
+15:
+Store transition Dr ← Dr ∪ {(s, a, s′)}
+16:
+end for
+17:
+for each policy updating step do
+18:
+Sample a minibatch of transitions (s, a, s′).
+19:
+Measure the confidence of reward models (Eq. 8)
+20:
+Relabel the transitions with ˆr(s, a; ψ) (Eq. 9)
+21:
+Update the policy π(s, a) on {(s, a, ˆr(s, a), s′)}
+22:
+end for
+23: end for
+To deal with the problem, an intuitive solution is to correct
+the predicted rewards before feeding them to the agent. Con-
+ventionally, methods such as reward shaping involve adding
+additional rewards or penalties to the original rewards to
+guide the agent toward the desired behavior. However, the
+added rewards usually introduce unintended side effects or
+inconsistencies in the learning process. As a mitigation, we
+propose to manipulate the rewards within a latent space,
+which avoids directly changing the predictions. We adopt
+an encoder-decoder structure where the encoder is used to
+map the input, i.e., a state-action pair, to latent space. After
+sampling a representation vector from the latent space, the
+decoder is applied to map the vector back to a reward.
+Formally, the encoder p(z|s, a; ψe), parameterized by ψe, is
+in the form of
+p(z|s, a; ψe) = N(z|f µ(s, a; ψe), f Σ(s, a; ψe)),
+(3)
+where N(µ, Σ) denotes a Gaussian distribution with mean
+vector µ and covariance matrix Σ. The encoder consists of
+two multi-layer perceptrons (MLPs) whose output gener-
+ates the K-dimensional mean µ and the K × K covariance
+matrix Σ, respectively. The decoder d(r|z; ψd), with pa-
+rameters ψd, takes as input a sampled latent variable z and
+outputs a reward. Such an encoder-decoder structure enjoys
+
+Reinforcement Learning from Diverse Human Preferences
+Figure 2. Examples for locomotion tasks and robotic manipulation
+tasks we test on.
+benefits under diverse human preferences: i) we can control
+the fluctuations of the rewards by adjusting the distribution
+of the latent space; ii) the confidence of the reward model
+to its predictions can be easily measured by calculating the
+divergence between different latent spaces. In the following
+sections, we will elaborate on how to leverage the aforemen-
+tioned advantages.
+3.2. Achieving Consistency by Imposing a Strong
+Constraint
+As previously mentioned, the reward model is learned under
+the supervision of human feedback, which could have high
+diversity if they are collected from different crowds. As a
+consequence, the rewards will demonstrate severe fluctua-
+tions and inconsistencies throughout the learning process.
+For example, at the beginning of the training, the reward
+model learns some patterns, and the policy is optimized to-
+ward the corresponding objective. As the training processes,
+more labeled preferences are added to the dataset and the
+updated reward model can be completely different. As a
+result, the reward model will make distinct predictions for
+the same input at the different training stages. We found
+that it is the temporal inconsistency that causes the collapse
+of a policy. To alleviate the problem, we propose to impose
+a constraint on the latent space so that the reward model
+has a fixed optimization direction throughout the training
+process. Concretely, we assume that the latent space fol-
+lows a prior distribution r(z), and we try to minimize the
+Kullback-Leibler (KL) divergence between the latent space
+and its prior:
+Lc = E(s,a)
+�
+KL(p(z|s, a; ψe)||r(z))
+�
+.
+(4)
+Since r(z) is pre-defined, the optimization of the encoder
+will be guided toward a fixed direction, independent of how
+diverse the human preferences are.
+Remark 3.1. Minimizing the loss in Eq. 4 is equivalent to
+minimizing the mutual information between (S, A) and Z,
+which leads to a concise representation of the input.
+Proof: To simplify the notation, we let variable X denote the
+input pairs (S, A). Then by the definition of KL-divergence:
+Lc =
+��
+dx dz p(x)
+�
+p(z|x) log p(z|x)
+r(z)
+�
+=
+��
+dx dz p(x, z) log p(z|x) −
+�
+dz p(z) log r(z).
+(5)
+Since KL(p(z)|r(z)) ≥ 0, we have
+�
+dz p(z) log p(z) ≥
+�
+dz p(z) log r(z). As a result,
+Lc ≥
+��
+dx dz p(x, z) log p(z|x) −
+�
+dz p(z) log p(z)
+= I(Z, X).
+(6)
+Eq. 6 shows that minimizing Lc is equivalent to minimizing
+an upper bound of I(Z, X).
+Overall, the loss function for the reward model is
+L = φ ∗ Lc + Ls,
+(7)
+where φ is a parameter controlling the strength of the con-
+straint. Conventionally, φ is set as a small value to confirm
+that the supervised signals will not be dominated. However,
+counterintuitively, we found that a large φ is crucial for
+good performance. Larger φ will lead to a stronger con-
+straint on the latent space. As a result, the latent space for
+different inputs will be similar, and the predicted rewards
+will be controlled into a smaller range. Considering that it
+is relative values of rewards, not absolute values, that affect
+a policy, a reward model with a smaller value range can
+lead to more accurate, stable, and effective outcomes, and
+therefore benefit the learning process.
+3.3. Confidence-based Reward Model Ensembling
+It is common that diverse human preferences contain out-
+lier data. To reduce the influence of a single data point on
+the reward model, we adopt reward model ensembling to
+reduce overfitting and improve stability (Lee et al., 2021b;
+Liang et al., 2022). Instead of simply averaging, we design
+a confidence-based ensembling mechanism to improve per-
+formance. The key idea is to aggregate the predicted results
+by up-weighting the reward models with higher confidence
+and down-weighting those with less confidence. We first
+measure the confidence level of each reward model and then
+perform a weighted summation to generate the final result.
+Specifically, the confidence of a reward model is measured
+by calculating the KL divergence from the predicted latent
+space to its prior distribution. If the KL divergence is small
+which means the reward model cannot tell too much input-
+specific information, the reward model has low confidence
+about the input (a model tends to output the prior directly
+
+Reinforcement Learning from Diverse Human Preferences
+0
+0.1M
+0.2M
+0.3M
+0.4M
+0.5M
+Environment Steps
+0
+250
+500
+750
+1000
+Episode Return
+Walker
+0
+0.2M
+0.4M
+0.6M
+0.8M
+1.0M
+Environment Steps
+0
+200
+400
+600
+Cheetah
+0
+0.2M
+0.4M
+0.6M
+0.8M
+1.0M
+Environment Steps
+0
+200
+400
+600
+800
+Quadruped
+0
+0.2M
+0.4M
+0.6M
+0.8M
+1.0M
+Environment Steps
+0
+25
+50
+75
+100
+Success Rate (%)
+Button Press
+0
+0.2M
+0.4M
+0.6M
+0.8M
+1.0M
+Environment Steps
+0
+25
+50
+75
+100
+Sweep Into
+0
+0.2M
+0.4M
+0.6M
+0.8M
+1.0M
+Environment Steps
+0
+25
+50
+75
+100
+Hammer
+Oracle
+Ours
+PEBBLE
+Figure 3. Learning curves on locomotion tasks (first row) and robotic manipulation tasks (second row). The locomotion tasks are measured
+on the ground truth episode return while the robotic manipulation tasks are measured on the success rate. The solid line and shaded
+regions represent the mean and standard deviation, respectively, across five runs.
+if it knows nothing about the input). On the contrary, a
+large KL divergence indicates a high confidence level. We
+assume that the confidence is proportional to the exponent
+of the KL divergence:
+Gi(s, a) =
+exp(KL(pi(z|s, a)||r(z)))
+�N
+j=1 exp(KL(pj(z|s, a)||r(z)))
+,
+(8)
+where Gi(s, a) denotes the confidence of the i-th reward
+model to an input (s, a), N is the number of reward mod-
+els. After determining the confidence of each model, we
+calculate the reward by:
+ˆr(s, a; ψ) =
+N
+�
+i=1
+Gi(s, a) ×
+�
+di ◦ qi(r|s, a)
+�
+,
+(9)
+where di and qi are the decoder and the encoder of the i-th
+reward model, respectively. With the reword model, we
+can use any preference-based RL algorithm to learn the
+policy. The full procedure of our method is summarized in
+Algorithm 1.
+4. Experiments
+We conduct experiments to answer the following questions:
+Q1: Whether the proposed method can effectively help ex-
+isting preference-based RL algorithms to learn from
+diverse preferences?
+Q2: How does each component of the method contribute to
+the effectiveness?
+Q3: How will latent spaces affect the predicted rewards?
+Q4: How will the method be affected by the number of
+annotators?
+4.1. Setup
+We evaluate our method on several complex locomotion
+tasks and robotic manipulation tasks from DeepMind Con-
+trol Suite (DMControl) (Tassa et al., 2018; Tunyasuvu-
+nakool et al., 2020) and Meta-world (Yu et al., 2020), respec-
+tively (see Fig. 2). In order to justify the effectiveness of our
+method, we train an agent to solve the tasks without observ-
+ing the true rewards from the environment. Instead, several
+scripted annotators are generated to provide their prefer-
+ences between two trajectory segments for the agent to learn
+its policy. Unlike existing preference-based RL algorithms
+which interact with a single perfect scripted teacher (Chris-
+tiano et al., 2017; Lee et al., 2021b; Park et al., 2022), we
+consider the situation where there is a team of different an-
+notators with bounded rationality to provide the preferences.
+Despite being imperfect, the annotators’ preferences are
+also calculated from ground truth rewards. Therefore, we
+can quantitatively evaluate the method by measuring the
+true episode return or success rate from the environments.
+Our method can be integrated into any preference-based
+RL algorithm to recover their performance under diverse
+preferences. In our experiments, we choose one of the most
+popular approaches, PEBBLE (Lee et al., 2021b), as the
+backbone algorithm. We examine the performance of PEB-
+BLE under i) a perfect scripted teacher who provides the
+ground true feedback (oracle); ii) a team of randomly sam-
+pled annotators whose feedback is imperfect and anisotropic.
+The goal of our method is to recover the performance of
+PEBBLE under the annotators as much as possible, to ap-
+
+Reinforcement Learning from Diverse Human Preferences
+0
+0.1M
+0.2M
+0.3M
+0.4M
+0.5M
+Environment Steps
+0
+500
+1000
+Episode Return
+Walker
+0
+0.2M
+0.4M
+0.6M
+0.8M
+1.0M
+Environment Steps
+0
+200
+400
+600
+Cheetah
+0
+0.2M
+0.4M
+0.6M
+0.8M
+1.0M
+Environment Steps
+0
+200
+400
+600
+Quadruped
+0
+0.2M
+0.4M
+0.6M
+0.8M
+1.0M
+Environment Steps
+0
+25
+50
+75
+100
+Success Rate (%)
+Button Press
+0
+0.2M
+0.4M
+0.6M
+0.8M
+1.0M
+Environment Steps
+0
+25
+50
+75
+100
+Sweep Into
+0
+0.2M
+0.4M
+0.6M
+0.8M
+1.0M
+Environment Steps
+0
+25
+50
+75
+100
+Hammer
+= 1
+= 10
+= 100
+Figure 4. Ablation study on the strength of the latent space constraint. The locomotion tasks (first row) are measured on the ground
+truth episode return while the robotic manipulation (second row) tasks are measured on the success rate. The results show the mean and
+standard deviation averaged over five runs.
+proach the oracle case.
+Simulating the annotators. We generate the bounded ratio-
+nal scripted annotators by following the previous stochastic
+preference model (Lee et al., 2021a):
+P
+�
+σ1 ≻ σ0�
+=
+exp
+�
+β �H
+t=1 γH−tr
+�
+s1
+t, a1
+t
+��
+�
+i∈{0,1} exp
+�
+β �H
+t=1 γH−tr
+�
+si
+t, ai
+t
+��.
+(10)
+r(s, a) is the ground truth reward provided by the envi-
+ronment. A scripted annotator is determined by a tuple
+⟨β, γ, ϵ, δequal⟩: β is the temperature parameter that con-
+trols the randomness of the stochastic preference model.
+An annotator becomes perfectly rational and deterministic
+as β → ∞, whereas β = 0 produces uniformly random
+choices. γ controls the myopic (short-sighted) behavior of
+an annotator. Annotators with small γ will emphasize more
+on immediate rewards and down-weight long-term return. ϵ
+describes the probability that an annotator makes a mistake,
+i.e., we flip the preference with the probability of ϵ. δequal de-
+notes the threshold that an annotator marks the segments as
+equally preferable, i.e., an annotator provides (0.5, 0.5) as a
+response if | �
+t r(s1
+t, a1
+t) − �
+t r(s0
+t, a0
+t)| ≤ δequal. Practi-
+cally, we sample a tuple from β ∈ {∞, 1, 5}, γ ∼ U(0.8, 1),
+ϵ ∼ U(0, 0.2), δequal ∼ U(0, 0.2) to generate a scripted an-
+notator. For each task, we randomly generate 100 annotators
+to provide feedback. Each annotator has the same probabil-
+ity of being selected for annotation.
+Implementation details. For all tasks, we use the same
+hyperparameters used by PEBBLE, such as learning rates,
+architectures of the neuron networks, and reward model
+updating frequency. We adopt an uniform sampling strat-
+egy, which selects queries with the same probability. At
+each feedback session, a batch of 256 trajectory segments
+(σ0, σ1) is sampled for annotation. The strength of con-
+straint φ is set as 100 for all tasks. For simplicity, we set the
+prior distribution of the latent space as standard Gaussian
+where the KL-divergence from a latent space to its prior can
+be easily calculated. All experimental results are reported
+with the mean and standard deviation across five runs.
+4.2. Experimental Results
+Locomotion tasks from DMControl.
+We select three
+complex environments from DMControl,
+which are
+Walker walk, Cheetah run, and Quadruped walk, to eval-
+uate our method. As previously mentioned, PEBBLE is
+used as the backbone algorithm and our method is com-
+bined with PEBBLE to recover its performance under di-
+verse human preferences. The first row of Fig. 3 shows the
+learning curves of PEBBLE and our method when learning
+from bounded rational annotators. We can find that, com-
+pared to learning from a single perfect teacher (oracle), the
+performance of PEBBLE (measure on true episode return)
+decreases dramatically in all three tasks. For example, in
+Walker walk, PEBBLE is able to achieve 1000 scores if
+it learns from a single expert, whereas the value is nearly
+half of the preferences are from different annotators. Such
+failures show that existing preference-based RL algorithms
+do not work well when the provided preferences contain
+diversity and inconsistency. After integrating our method
+(the red line), we can find significant performance increases
+in all three tasks: our method is able to achieve almost the
+same performance as the oracle in Walker walk, while the
+performance gap between our method and its upper bound
+
+Reinforcement Learning from Diverse Human Preferences
+Figure 5. Analysis about the influence of φ on the reward model. First row: increasing the strength of the constraint will narrow the
+value range of the predicted rewards. The reward model will also generate more distinct predictions if φ is large. Second row: the t-SNE
+visualization of the latent vectors. A large φ leads to a more compact and concise pattern.
+(oracle) is very narrow in Cheetah run. In Quadruped walk,
+PEBBLE is unable to learn a feasible policy, while our
+proposed method still achieves near-optimal performance.
+Robotic manipulation tasks from Meta-world.
+Meta-
+world consists of 50 tasks that cover a range of fundamental
+robotic manipulation skills. We consider three challenging
+environments to evaluate the effectiveness of our method.
+The performance is measured on success rate, i.e., if the
+trained agent is able to successfully finish a task or not. Fig 3
+(second row) shows the learning curves of our method as
+the baselines. We can find that there is a significant perfor-
+mance increase after integrating our method into PEBBLE.
+The performance can be almost restored to approach the
+oracles in Button Press and Hammer, while in Sweep Into,
+the improvement is also non-trivial. These results again
+demonstrate that our proposed method is able to effectively
+help the existing preference-based RL algorithms learn from
+diverse preferences.
+4.3. Ablation and Analysis
+Effects of the latent space constraint. As previously in-
+troduced, to achieve temporal consistency and set a fixed
+optimization direction for the reward model, our method
+imposes a constraint on the latent space by forcing its dis-
+tribution to be close to the prior. To justify the effect of
+the constraint, we implement our method with different
+strengths of constraint on all six tasks. As shown in Fig. 4,
+there is a significant and consistent improvement in all the
+tasks as we gradually increase the strength of the constraint.
+For example, in Cheetah run, when we set the strength of
+0
+100K
+200K
+300K
+400K
+500K
+Environment Steps
+0
+200
+400
+600
+800
+1000
+Episode Return
+w/ ensembling
+w/o ensembling
+0
+100K
+200K
+300K
+400K
+500K
+Environment Steps
+0
+200
+400
+600
+800
+1000
+KL-based
+mean
+Figure 6. Ablation study on reward model ensembling.
+Left:
+Learning curves of Walker walk with and without reward model
+ensembling. Right: Learning curves of Walker walk with KL-
+based model ensembling and simply averaging. The results show
+the mean and standard deviation averaged over five runs.
+constraint ψ to 1, 10, and 100, the performance increases
+from around 200 to 400 and finally reaches near 600. This
+phenomenon is a little bit counter-intuitive because, con-
+ventionally, a too strong constraint is likely to misguide
+the reward model and prevent it from learning from super-
+vised signals. However, we found that a strong constraint on
+the latent space is compulsory to help an agent learn from
+diverse feedback.
+Analysis about the reward model. To understand why a
+strong constraint is crucial for the performance, we ana-
+lyze the effect of the latent space constraint on the reward
+model. Specifically, we collect 100,000 state-action pairs
+from Cheetah run at different training stages and use the
+reward model trained with different strengths of constraint
+to predict the rewards. The predictions are presented in
+
+Φ=l
+Φ=10
+Φ= 100
+Predicted Rewards
+0.2
+0.0
+0.0 
+0.0
+-0.2
+-0.2
+-0.2
+-0.4
+-0.4
+-0.4
+-0.6
+-0.6
+100
+100
+100
+50
+50
+50
+tSNE2
+0
+0
+-50
+-50
+-50
+-100
+-100
+-100
+-100
+-50
+0
+50
+100
+-100
+-50
+50
+100
+-100
+-50
+0
+50
+100
+0
+tSNE1
+tSNE1
+tSNE1Reinforcement Learning from Diverse Human Preferences
+0
+0.2M
+0.4M
+0.6M
+0.8M
+1.0M
+Environment Steps
+0
+200
+400
+600
+800
+Episode Return
+Num_annotators=1
+0
+0.2M
+0.4M
+0.6M
+0.8M
+1.0M
+Environment Steps
+0
+200
+400
+600
+800
+Num_annotators=10
+0
+0.2M
+0.4M
+0.6M
+0.8M
+1.0M
+Environment Steps
+0
+200
+400
+600
+800
+Num_annotators=100
+Oracle
+Ours
+PEBBLE
+Figure 7. Learning curves of Cheetah run (a locomotion task) with preferences provided by a different number of annotators. The results
+are measured on the ground truth episode return, with the solid line and shaded regions representing the mean and standard deviation,
+respectively, across five runs.
+the first row of Fig. 5. We can find that as we increase the
+strength of constraint, the range of reward values decreases
+gradually. For example, when φ = 1, the predicted rewards
+are between -0.6 and 0.15, while the range is narrowed to
+[−0.5, 0] when we set φ = 100. Moreover, the predicted
+rewards are more distinct when φ becomes larger, which
+indicates that only really good state-action pairs are given
+high rewards. We also use t-SNE (Van der Maaten & Hin-
+ton, 2008) to visualize the latent vector of those state-action
+pairs. As in Fig. 5 (second row), the distribution of the
+embeddings becomes more compact as we increase φ. Fur-
+thermore, the pattern of the embeddings is more clear and
+more concise when φ is large.
+Effects of reward model ensembling. We investigate how
+well the reward ensembling affects the performance of
+our method. Fig. 6 (left) shows the learning curves of
+Walker walk with and without reward model ensembling.
+We can find that there is a clear performance drop if using a
+single reward model. The results demonstrate that ensem-
+bling the predictions of several models is helpful to stabilize
+the training process if the preferences are diverse. We fur-
+ther investigate whether the proposed KL-based aggregation
+method is better than simply averaging. As shown in Fig. 6
+(right), simply averaging will suffer severe fluctuations in
+the training process, while the performance of our method
+is significantly more stable and consistent.
+Responses to the number of annotators. To examine how
+will our algorithm respond to the number of annotators, we
+implement Cheetah run with preferences provided by dif-
+ferent numbers of annotators. As shown in Fig 7, when
+there is only one annotator which is bounded rational, both
+PEBBLE and our method perform worse than the oracle. In
+these cases, the preferences are not diverse but just partially
+correct. If we slightly increase the number of annotators
+to ten, which introduces some diversity, our method is able
+to achieve obvious improvement over PEBBLE. The per-
+formance gain becomes quite significant when there are
+one hundred annotators. The experiments demonstrate that
+our method is suitable for situations where the provided
+preferences are diverse.
+5. Related Work
+The main focus in the paper is on one promising direction
+which utilizes human preferences (Akrour et al., 2011; Chris-
+tiano et al., 2017; Ibarz et al., 2018; Leike et al., 2018; Lee
+et al., 2021b; Ouyang et al., 2022; Park et al., 2022; Liang
+et al., 2022) to perform policy optimization. Christiano
+et al. (2017) introduced modern deep learning techniques
+to preference-based learning. Since the learning of the re-
+ward function, modeled by deep neural networks, requires
+a large number of preferences, recent works have typically
+focused on improving the feedback efficiency of a method.
+PEBBLE (Lee et al., 2021b) proposed a novel unsupervised
+exploration method to pre-train the policy. SURF (Park
+et al., 2022) adopted a semi-supervised reward learning
+framework to leverage a large number of unlabeled samples.
+Some other works improved data efficiency by introducing
+additional types of feedback such as demonstrations (Ibarz
+et al., 2018) or non-binary rankings (Cao et al., 2021). In
+addition to that, designing intrinsic rewards to encourage
+effective exploration is also investigated (Liang et al., 2022).
+Despite being efficient, previous methods mainly focus on
+learning from a single expert, which will severely limit the
+scalability of an algorithm. In this work, we focus on learn-
+ing from human preferences collected from different types
+of annotators. Our method emphasizes addressing the issue
+of diversity rather than feedback efficiency.
+6. Conclusion
+In this work, we propose a simple yet effective method
+to improve the performance of preference-based RL algo-
+rithms under diverse feedback. The method maps inputs to
+a latent space imposes a constraint on the latent space to
+
+Reinforcement Learning from Diverse Human Preferences
+maintain temporal consistency, and uses a confidence-based
+ensembling method to generate more stable predictions. Ex-
+tensive experiments are conducted in various environments.
+The results show that our method can significantly improve
+performance under diverse preferences in all the tasks.
+References
+Akrour, R., Schoenauer, M., and Sebag, M. Preference-
+based policy learning. In Joint European Conference
+on Machine Learning and Knowledge Discovery in
+Databases, pp. 12–27. Springer, 2011.
+Biyik, E. and Sadigh, D. Batch active preference-based
+learning of reward functions. In Conference on Robot
+Learning, pp. 519–528. PMLR, 2018.
+Bradley, R. A. and Terry, M. E. Rank analysis of incom-
+plete block designs: I. the method of paired comparisons.
+Biometrika, 39(3/4):324–345, 1952.
+Cao, Z., Wong, K., and Lin, C.-T. Weak human preference
+supervision for deep reinforcement learning. IEEE Trans-
+actions on Neural Networks and Learning Systems, 32
+(12):5369–5378, 2021.
+Christiano, P. F., Leike, J., Brown, T., Martic, M., Legg,
+S., and Amodei, D. Deep reinforcement learning from
+human preferences. Advances in neural information pro-
+cessing systems, 30, 2017.
+Gerstgrasser, M., Trivedi, R., and Parkes, D. C. Crowdplay:
+Crowdsourcing human demonstrations for offline learn-
+ing. In International Conference on Learning Represen-
+tations, 2022. URL https://openreview.net/
+forum?id=qyTBxTztIpQ.
+Hejna III, D. J. and Sadigh, D. Few-shot preference learning
+for human-in-the-loop rl. In 6th Annual Conference on
+Robot Learning, 2022.
+Ibarz, B., Leike, J., Pohlen, T., Irving, G., Legg, S., and
+Amodei, D. Reward learning from human preferences and
+demonstrations in atari. Advances in Neural Information
+Processing Systems, 31, 2018.
+Lee, K., Smith, L., Dragan, A., and Abbeel, P. B-pref:
+Benchmarking preference-based reinforcement learning.
+In Thirty-fifth Conference on Neural Information Process-
+ing Systems Datasets and Benchmarks Track (Round 1),
+2021a.
+Lee, K., Smith, L. M., and Abbeel, P. Pebble: Feedback-
+efficient interactive reinforcement learning via relabeling
+experience and unsupervised pre-training. In Proceed-
+ings of the 38th International Conference on Machine
+Learning, pp. 6152–6163, 2021b.
+Leike, J., Krueger, D., Everitt, T., Martic, M., Maini, V., and
+Legg, S. Scalable agent alignment via reward modeling:
+a research direction. arXiv preprint arXiv:1811.07871,
+2018.
+Liang, X., Shu, K., Lee, K., and Abbeel, P. Reward uncer-
+tainty for exploration in preference-based reinforcement
+learning. In International Conference on Learning Rep-
+resentations, 2022.
+Mnih, V., Kavukcuoglu, K., Silver, D., Rusu, A. A., Veness,
+J., Bellemare, M. G., Graves, A., Riedmiller, M., Fidje-
+land, A. K., Ostrovski, G., et al. Human-level control
+through deep reinforcement learning. Nature, 518(7540):
+529–533, 2015.
+Moravˇc´ık, M., Schmid, M., Burch, N., Lis`y, V., Morrill, D.,
+Bard, N., Davis, T., Waugh, K., Johanson, M., and Bowl-
+ing, M. Deepstack: Expert-level artificial intelligence in
+heads-up no-limit poker. Science, 356(6337):508–513,
+2017.
+Ouyang, L., Wu, J., Jiang, X., Almeida, D., Wainwright,
+C. L., Mishkin, P., Zhang, C., Agarwal, S., Slama,
+K., Ray, A., et al.
+Training language models to fol-
+low instructions with human feedback. arXiv preprint
+arXiv:2203.02155, 2022.
+Park, J., Seo, Y., Shin, J., Lee, H., Abbeel, P., and Lee,
+K. SURF: Semi-supervised reward learning with data
+augmentation for feedback-efficient preference-based re-
+inforcement learning. In International Conference on
+Learning Representations, 2022.
+Silver, D., Huang, A., Maddison, C. J., Guez, A., Sifre, L.,
+Van Den Driessche, G., Schrittwieser, J., Antonoglou, I.,
+Panneershelvam, V., Lanctot, M., et al. Mastering the
+game of go with deep neural networks and tree search.
+Nature, 529(7587):484–489, 2016.
+Silver, D., Hubert, T., Schrittwieser, J., Antonoglou, I., Lai,
+M., Guez, A., Lanctot, M., Sifre, L., Kumaran, D., Grae-
+pel, T., et al. A general reinforcement learning algorithm
+that masters chess, shogi, and go through self-play. Sci-
+ence, 362(6419):1140–1144, 2018.
+Silver, D., Singh, S., Precup, D., and Sutton, R. S. Reward
+is enough. Artificial Intelligence, 299:103535, 2021.
+Stiennon, N., Ouyang, L., Wu, J., Ziegler, D., Lowe, R.,
+Voss, C., Radford, A., Amodei, D., and Christiano,
+P. F. Learning to summarize with human feedback. Ad-
+vances in Neural Information Processing Systems, 33:
+3008–3021, 2020.
+Tassa, Y., Doron, Y., Muldal, A., Erez, T., Li, Y., Casas, D.
+d. L., Budden, D., Abdolmaleki, A., Merel, J., Lefrancq,
+A., et al.
+Deepmind control suite.
+arXiv preprint
+arXiv:1801.00690, 2018.
+
+Reinforcement Learning from Diverse Human Preferences
+Tunyasuvunakool, S., Muldal, A., Doron, Y., Liu, S., Bohez,
+S., Merel, J., Erez, T., Lillicrap, T., Heess, N., and Tassa,
+Y. dm control: Software and tasks for continuous control.
+Software Impacts, 6:100022, 2020.
+Van der Maaten, L. and Hinton, G. Visualizing data using
+t-sne. Journal of Machine Learning Research, 9(11),
+2008.
+Vinyals, O., Babuschkin, I., Czarnecki, W. M., Mathieu, M.,
+Dudzik, A., Chung, J., Choi, D. H., Powell, R., Ewalds,
+T., Georgiev, P., et al. Grandmaster level in starcraft ii
+using multi-agent reinforcement learning. Nature, 575
+(7782):350–354, 2019.
+Wilson, A., Fern, A., and Tadepalli, P. A bayesian approach
+for policy learning from trajectory preference queries.
+Advances in Neural Information Processing Systems, 25,
+2012.
+Wurman, P. R., Barrett, S., Kawamoto, K., MacGlashan, J.,
+Subramanian, K., Walsh, T. J., Capobianco, R., Devlic,
+A., Eckert, F., Fuchs, F., et al. Outracing champion gran
+turismo drivers with deep reinforcement learning. Nature,
+602(7896):223–228, 2022.
+Yu, T., Quillen, D., He, Z., Julian, R., Hausman, K., Finn,
+C., and Levine, S. Meta-world: A benchmark and evalua-
+tion for multi-task and meta reinforcement learning. In
+Conference on Robot Learning, pp. 1094–1100. PMLR,
+2020.
+

4dFIT4oBgHgl3EQf6yuB/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7171eb31177c26face7730f48e1ed5fa2620a66adc313299de2a4a108019b08b
+size 2687021

4dFIT4oBgHgl3EQf6yuB/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f2b5f7bd73608b6c809b18475017412a0ffc26099289425272a1c9399086a900
+size 87709

6tAzT4oBgHgl3EQfgPwz/content/2301.01464v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3a0d78a16f9953dcd882e3e89995f1fd2f7a19bdf1f6878d74db9a1132c8949d
+size 1108418

6tE2T4oBgHgl3EQfkwcv/content/tmp_files/2301.03981v1.pdf.txt

@@ -0,0 +1,617 @@
+The Lüscher scattering formalism on the 𝒕-channel cut
+André Baião Raposo𝑎,∗ and Maxwell T. Hansen𝑎
+𝑎Higgs Centre for Theoretical Physics, School of Physics and Astronomy,
+The University of Edinburgh, Edinburgh EH9 3FD, UK
+E-mail: [email protected], [email protected]
+The Lüscher scattering formalism, the standard approach for relating the discrete finite-volume
+energy spectrum to two-to-two scattering amplitudes, fails when analytically continued so far below
+the infinite-volume two-particle threshold that one encounters the 𝑡-channel cut. This is relevant,
+especially in baryon-baryon scattering applications, as finite-volume energies can be observed in
+this below-threshold regime, and it is not clear how to make use of them. In this talk, we present a
+generalization of the scattering formalism that resolves this issue, allowing one to also constrain
+scattering amplitudes on the 𝑡-channel cut.
+39th International Symposium on Lattice Field Theory - Lattice2022
+8-13 August 2022
+Bonn, Germany
+∗Speaker
+© Copyright owned by the author(s) under the terms of the Creative Commons
+Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0).
+https://pos.sissa.it/
+arXiv:2301.03981v1  [hep-lat]  10 Jan 2023
+
+The Lüscher scattering formalism on the 𝑡-channel cut
+André Baião Raposo
+1.
+Introduction & motivation
+In recent years, there has been considerable progress in the determination of two-nucleon and
+other two-baryon scattering amplitudes using numerical lattice QCD [1–9]. One of the leading
+methods in these calculations is to first extract the finite-volume energy spectrum and subsequently
+the scattering amplitudes via the Lüscher formalism and its extensions [10–20]. In such calculations,
+each finite-volume energy level constrains or predicts the scattering matrix for all multi-hadron
+channels that can physically propagate at that energy.
+One limitation in all finite-volume formalisms published to date is the neglect of volume effects
+associated with the 𝑡-channel (also called left-hand) cuts.1 This is most obviously a problem when
+the lattice calculation predicts energies that are on top of the cut, as has recently been seen in
+ref. [7]. The finite-volume formalism is manifestly not applicable here, as it leads to predictions of a
+real-valued K-matrix (equivalently, a real-valued scattering phase shift) in a region where the latter
+is known to be complex.
+In this proceedings, we present an extension of the original formalism that can be applied on
+the left-hand cut. We begin with a brief review of infinite-volume scattering theory as well as the
+standard Lüscher formalism, in sections 2 and 3, respectively. In section 4, we illustrate how the
+𝑡-channel cut becomes an issue and, in section 5, we briefly describe our approach to a solution, the
+full details of which will be presented in a publication (to appear). Conclusions and an outlook are
+given in section 6.
+2.
+Two-to-two scattering in infinite-volume
+We start by reviewing a few properties of scattering amplitudes in the infinite-volume context,
+making no reference yet to the finite-volume formalism. Considering two-to-two elastic scattering
+of non-identical mass-degenerate spin-zero particles with physical mass 𝑀, we write the total
+four-momentum in a given frame as 𝑃 = (𝐸, 𝑷) and introduce the standard Mandelstam invariants
+𝑠 and 𝑡. Mandelstam 𝑠 satisfies 𝑠 = 𝑃2 = 𝐸2 − 𝑷2 = (𝐸★)2, where 𝐸★ denotes the centre-of-mass
+frame energy. Note we will use ★ to denote quantities boosted to the centre-of-mass frame.
+The scattering amplitude, which we write M(𝑠, 𝑡), can be formally expressed as the sum of
+all connected and amputated two-to-two Feynman diagrams, with legs amputated and set on the
+mass shell (i.e. with external momenta 𝑝 having 𝑝2 = (𝑝0)2 − 𝒑2 = 𝑀2). This all-orders sum can
+be organized by introducing the Bethe-Salpeter kernel, defined as the sum of all connected and
+amputated two-to-two diagrams that are two-particle irreducible in the 𝑠-channel2. The amplitude
+is then expressible in terms of the Bethe-Salpeter kernels and pairs of dressed propagators of the
+scattering scalars, as shown in figure 1. Note that all propagators considered are taken with the
+standard 𝑖𝜖 prescription, and all loop momenta are integrated over all components.
+1For ref. [21], the issue of the cut may be circumvented by working in the plane-wave basis, but this is not specifically
+discussed in those proceedings.
+2In other words, the Bethe-Salpeter kernel is built from diagrams that cannot be separated into two pieces by cutting
+through two propagators whose momenta sum to the total four-momentum 𝑃 = (𝐸, 𝑷).
+2
+
+The Lüscher scattering formalism on the 𝑡-channel cut
+André Baião Raposo
+Figure 1: (a) Diagrammatic representation of the two-to-two scattering amplitude using Bethe-Salpeter
+kernels and dressed propagators. (b) De��nition of the Bethe-Salpeter kernel as the sum of all connected
+and amputated two-to-two diagrams which are two-particle irreducible in the 𝑠-channel; we assume that
+self-interactions of the scattering particles are Z2-invariant, such that we consider vertices with even number
+of legs only, while dashed lines denote other particles that might couple to the scattering channels of interest.
+(c) Definition of the dressed propagator in terms of bare propagators and self-energy kernels. (d) Definition of
+the self-energy as the sum of all one-particle irreducible diagrams, with dashed lines again denoting other
+particle types that can couple to the scattering particles.
+It is also instructive to define partial-wave amplitudes according to
+M(𝑠, 𝑡) =
+∞
+∑︁
+ℓ=0
+𝑃ℓ(cos 𝜃★)Mℓ(𝑠) ,
+(1)
+where 𝑃ℓ is a Legendre polynomial and 𝜃★ is the scattering angle in the centre-of-mass frame,
+satisfying sin2(𝜃★/2) = −𝑡/(𝑠 − 4𝑀2).
+Using the all-orders Bethe-Salpeter representation (as discussed below) or constraints based
+on the unitarity of the scattering matrix, one can show that the imaginary part of Mℓ(𝑠)−1 is
+independent of the details of particle interactions. The real part is then typically parameterized using
+the scattering phase shift 𝛿ℓ(𝑠). We may write
+Im Mℓ(𝑠)−1 = −𝜌(𝑠) Θ(𝐸★ − 2𝑀) ,
+(2)
+Re Mℓ(𝑠)−1 = 𝜌(𝑠) cot 𝛿ℓ(𝑠) ≡ Kℓ(𝑠)−1 ,
+(3)
+where 𝜌(𝑠) ≡
+𝑝★
+8𝜋𝐸★ is the phase-space factor for non-identical particles, with 𝑝★ ≡ 1
+2
+√
+𝑠 − 4𝑀2
+denoting each particle’s centre-of-mass spatial momentum magnitude, and we have defined the
+K-matrix Kℓ(𝑠). This leads to the standard form of the partial-wave amplitude
+Mℓ(𝑠) =
+1
+Kℓ(𝑠)−1 − 𝑖𝜌(𝑠) =
+8𝜋𝐸★
+𝑝★ cot 𝛿ℓ − 𝑖𝑝★ .
+(4)
+One can also reach these results via the Bethe-Salpeter series of figure 1 if one defines the
+K-matrix K by the same series as the amplitude M, but in which all two-particle loops are evaluated
+with a principal-value prescription instead of the 𝑖𝜖 prescription. The definitions of M and K can
+3
+
+The Lüscher scattering formalism on the 𝑡-channel cut
+André Baião Raposo
+then be related by writing each 𝑖𝜖-loop in terms of its real and imaginary parts. The former coincides
+with the principal-value loop integral, and the latter leads to a Dirac delta function, allowing the
+loop integral to be exactly evaluated.
+We should emphasize that these relations hold only for (2𝑀)2 < 𝑠 < (𝐸★
+inel.)2 where 𝐸inel. is
+the energy of the lowest-lying inelastic threshold coupling to the channel of interest. This fact has
+received significant attention for energies above 𝐸inel. (in the form of three-particle finite-volume
+formalisms [22–27]), but in this work we are concerned with the range 𝑠 < (2𝑀)2. For these
+sub-threshold energies, one can analytically continue the amplitude by taking −𝑖𝜌(𝑠) → |𝜌(𝑠)| in
+order to remain on the physical Riemann sheet.
+Such analytic continuation leads to a real-valued scattering amplitude, provided that the K-matrix
+is real. When, however, we have a lighter particle that couples to the scattering channel of interest,
+the K-matrix partial waves become complex-valued due to a sub-threshold branch cut, the so-called
+𝑡-channel or left-hand cut. Before turning to the consequences of the cut, we review the standard
+finite-volume formalism of Lüscher and show that a real-valued K-matrix is implicitly assumed in
+the sub-threshold analytic continuation, and thus that the formalism is not applicable on the left-hand
+cut.
+3.
+Review of the Lüscher formalism
+In this section, we review the derivation of the Lüscher quantization condition [10], which has
+been subsequently extended in refs. [11–20] to include all types of coupled two-particle channels.
+We focus here on the case of a single channel with two mass-degenerate but non-identical spin-zero
+particles.
+Consider a quantum field theory defined in a finite cubic spatial volume of side-length 𝐿, with
+periodic boundary conditions. This system then has a discrete 𝐿-dependent energy spectrum, and
+the energies lying below the lowest-lying three- or four-particle threshold can be used to extract the
+elastic two-to-two scattering amplitude. We follow closely the derivation of Kim, Sachrajda and
+Sharpe [13], also used in refs. [17, 28–30]. We begin by defining a two-point correlation function
+𝐶𝐿(𝐸, 𝑷) =
+∫
+𝑑𝑥0
+∫
+𝐿
+𝑑3𝒙 𝑒−𝑖𝐸𝑥0𝑒𝑖𝑷·𝒙⟨0|TA(𝑥)A†(0)|0⟩𝐿 ,
+(5)
+where the subscript 𝐿 in
+∫
+𝐿 𝑑3𝒙 indicates that the integral runs over the finite volume, 𝐸 denotes the
+total energy, 𝑷 is the total spatial momentum, and A(𝑥) and A†(𝑥) are annihilation and creation
+operators carrying the quantum numbers of the scattering channel of interest.
+One can construct a diagrammatic representation for this correlator using the ingredients already
+introduced in the previous section, the Bethe-Salpeter kernel and the dressed propagator pairs. This
+is known as the skeleton expansion for the correlator and is shown in figure 2. In finite volume,
+spatial loop momenta are discretized as 𝒌 = 2𝜋
+𝐿 𝒏, with 𝒏 ∈ Z3, and we have spatial loop momentum
+sums instead of integrals, i.e. we replace
+∫
+𝑑3𝒌
+(2𝜋)3 →
+1
+𝐿3
+�
+𝒌 ∈(2𝜋/𝐿)Z3 in all loops.
+The key observation for deriving the Lüscher formalism is that not all loops have the same
+volume dependence: loops with intermediate states that cannot go on shell in the energy range
+considered have exponentially suppressed volume effects O(𝑒−𝑚𝐿), with 𝑚 being the mass of the
+lightest particle coupled to the system, while loops with intermediate states that can go on shell
+4
+
+The Lüscher scattering formalism on the 𝑡-channel cut
+André Baião Raposo
+Figure 2: Skeleton-expansion representation of the finite-volume correlator 𝐶𝐿(𝐸, 𝑷), in terms of Bethe-
+Salpeter kernels and dressed propagators, as defined in figure 1. The end-cap “blobs” stand for functions
+in momentum-space originating from the Fourier transforms of the creation and annihilation operators. As
+discussed, one can take the kernels and dressed propagators in the expansion to be the infinite-volume objects,
+as the difference between these and their finite-volume counterparts is exponentially suppressed, and thus only
+the loops explicitly shown need to be treated as finite-volume loops.
+receive power-like effects O(𝐿−𝑛), for some non-negative integer 𝑛. In the elastic regime, i.e. for
+centre-of-mass frame energies above the two-particle threshold but below the thresholds of all other
+channels, on-shell states come precisely from the loops left explicit in the skeleton expansion shown
+in figure 2. Every other loop, implicitly included in either the Bethe-Salpeter kernels or the dressed
+propagators, may be replaced by its infinite-volume counterpart, as the difference, which we neglect,
+is exponentially suppressed in 𝐿. Thus, we effectively replace the finite-volume Bethe-Salpeter
+kernels and dressed propagators with their infinite-volume counterparts.
+Consider one of the two-particle loops shown in the expansion of figure 2. Its contribution can
+be written as
+𝐶loop
+𝐿
+(𝑃) =
+∫
+𝑑𝑘0
+2𝜋
+1
+𝐿3
+∑︁
+𝒌
+L(𝑃, 𝑘) Δ(𝑘) Δ(𝑃 − 𝑘) R∗(𝑃, 𝑘) ,
+(6)
+with 𝑃 ≡ (𝐸, 𝑷) and loop momentum 𝑘 ≡ (𝑘0, 𝒌). The functions L and R∗ stand for the objects
+before and after the given loop, Δ is a fully dressed scalar propagator (defined to have unit residue at
+each pole). Performing the 𝑘0-integral and decomposing L and R in spherical harmonics with 𝑘
+individually put on shell, i.e. setting 𝑘 = (𝜔(𝒌), 𝒌) with 𝜔(𝒌) ≡
+√︁
+𝒌2 + 𝑀2, we can obtain
+𝐶loop
+𝐿
+(𝑃) = 1
+𝐿3
+∑︁
+𝒌
+Lℓ𝑚(𝑃, |𝒌★|) 𝑖Sℓ𝑚;ℓ′𝑚′(𝑃, 𝒌; 𝐿) R∗
+ℓ′𝑚′(𝑃, |𝒌★|) + 𝑟(𝑃) ,
+(7)
+where we have introduced
+Sℓ𝑚;ℓ′𝑚′(𝑃, 𝒌; 𝐿) ≡
+4𝜋𝑌ℓ𝑚( ˆ𝒌★) 𝑌∗
+ℓ′𝑚′( ˆ𝒌★) 𝐻(𝒌★)
+2𝜔(𝒌) 2𝜔(𝑷 − 𝒌) (𝐸 − 𝜔(𝒌) − 𝜔(𝑷 − 𝒌))
+� |𝒌★|
+𝑘★
+os
+�ℓ+ℓ′
+,
+(8)
+for later convenience. Note also that sums over the repeated indices ℓ, 𝑚 and ℓ′, 𝑚′ are implied.
+The term 𝑟(𝑃) in eq. (7) is a sum over a smooth summand, leading to exponentially suppressed
+finite-volume corrections, which we may neglect. The summand in the first term and, more
+specifically, the quantities Sℓ𝑚;ℓ′𝑚′(𝑃, 𝒌; 𝐿), contain the pole corresponding to the two-particle
+intermediate state going on-shell, as can be seen explicitly in eq. (8), and thus this term contains all
+the power-like volume dependence arising from the loop we are considering.
+In eq. (8), we use the notation 𝑘★
+os for the value of |𝒌★| which satisfies the intermediate
+two-particle state on-shell condition 𝐸★ = 2𝜔(𝒌★), equivalent to 𝐸 = 𝜔(𝒌) + 𝜔(𝑷 − 𝒌), given by
+the simple relation
+𝑘★
+os ≡ 1
+2
+√︁
+𝑠 − 4𝑀2 = 1
+2
+√︁
+𝐸2 − 𝑷2 − 4𝑀2 .
+(9)
+5
+
+The Lüscher scattering formalism on the 𝑡-channel cut
+André Baião Raposo
+Note that this relation fixes the magnitude of 𝒌★ at the pole, but not its direction. The barrier
+factor �|𝒌★|/𝑘★
+os
+�ℓ+ℓ′
+is introduced to ensure that no singularities arise from the spherical harmonics
+𝑌ℓ𝑚( ˆ𝒌★) and 𝑌∗
+ℓ′𝑚′( ˆ𝒌★).
+The function 𝐻(𝒌★) is a regulator function that takes a value of 1 for 4𝜔(𝒌★)2 = 4(|𝒌★|2+𝑀2) <
+(𝐸★
+inel.)2 and of 0 for 4𝜔(𝒌★)2 = 4(|𝒌★|2 + 𝑀2) > (𝐸★
+uv)2, where again 𝐸inel. is the lowest lying three-
+or four-particle threshold, and 𝐸★
+uv is some chosen high ultraviolet cut-off. In the region between,
+𝐻(𝒌★) interpolates smoothly between the two values. This regulator function is similar to the one
+found in the three-body scattering formalism of refs. [22, 23], and corresponds to a separation of
+low-energy and high-energy parts of the sum, such that both parts are regulated and kept finite.3
+We next reduce eq. (7) by expanding the functions Lℓ𝑚(𝑃, |𝒌★|) and R∗
+ℓ′𝑚′(𝑃, |𝒌★|) about
+|𝒌★| = 𝑘★
+os and subtracting and adding an integral to reach
+𝐶loop
+𝐿
+(𝑃) = Lℓ𝑚(𝑃, 𝑘★
+os) 𝑖𝐹ℓ𝑚;ℓ′𝑚′(𝑃; 𝐿) R∗
+ℓ′𝑚′(𝑃, 𝑘★
+os) + 𝑟′(𝑃) ,
+= Los(𝑃) 𝑖𝐹(𝑃; 𝐿) R†
+os(𝑃) + 𝑟′(𝑃) ,
+(10)
+where we introduce the sum-integral difference
+𝐹ℓ𝑚;ℓ′𝑚′(𝑃; 𝐿) =
+�
+1
+𝐿3
+∑︁
+𝒌
+− p.v.
+∫
+𝑑3𝒌
+(2𝜋)3
+�
+Sℓ𝑚;ℓ′𝑚′(𝑃, 𝒌; 𝐿) .
+(11)
+Here, p.v. means the integral is evaluated using a principal-value prescription. The remainder term
+𝑟′(𝑃) differs from 𝑟(𝑃), but still has the property that it contains the sum of a smooth summand
+together with integrals. In the second line of eq. (10), we have defined a compact vector-matrix
+notation in the angular-momentum index space.
+Applying this procedure iteratively to all loops in the skeleton expansion diagrams, it can be
+shown that we may write the finite-volume correlator in the form:
+𝐶𝐿(𝑃) =
+∞
+∑︁
+𝑛=0
+𝐴(𝑃) 𝑖𝐹(𝑃; 𝐿) [𝑖K(𝑃) 𝑖𝐹(𝑃; 𝐿)]𝑛 𝐴†(𝑃) + 𝐶∞(𝑃) .
+(12)
+The quantities in the first term are vectors or matrices in angular momentum index space: 𝐴(𝑃) and
+𝐴†(𝑃) are smooth vectors loosely corresponding to the source and sink operators and K(𝑃) is the
+K-matrix introduced in the previous section (note that K is an infinite-volume scalar, and thus only
+depends on 𝑠 = 𝑃2, but we keep 𝑃 as an argument for compactness of notation). Noting that the
+above is a geometric series, we can sum it to obtain
+𝐶𝐿(𝑃) = 𝐴(𝑃)
+𝑖
+𝐹−1(𝑃; 𝐿) + K(𝑃) 𝐴†(𝑃) + 𝐶∞(𝑃) .
+(13)
+Given that we neglect exponentially suppressed volume effects, the volume dependence is entirely
+contained in the 𝐹(𝑃; 𝐿) matrix.
+3It should be emphasized that we have renormalization and regularization schemes keeping the overall result finite, the
+regulator function here simply ensures we have a separation of high-energy and low-energy contributions to the sum such
+that both parts are finite and that the low-energy part, which contains the relevant singular behaviour, is tractable when
+implemented numerically. 𝐸uv will simply be a scheme-dependence of the formalism, but should be kept high, as setting
+it too low will lead to enhanced finite-volume effects.
+6
+
+The Lüscher scattering formalism on the 𝑡-channel cut
+André Baião Raposo
+Using a spectral representation of the correlator, it is straightforward to show that it must have
+poles at the energy levels of the finite-volume spectrum 𝐸𝑛(𝑷; 𝐿). These poles in 𝐶𝐿(𝐸, 𝑷) can
+only arise from the 𝐿-dependent part of the first term, meaning that we must have
+det
+�
+𝐹−1(𝐸𝑛(𝑷; 𝐿), 𝑷; 𝐿) + K(𝐸𝑛(𝑷; 𝐿), 𝑷)
+�
+= 0 ,
+(14)
+at all finite-volume energy levels. This is called the Lüscher quantization condition, and it can be
+used to determine K, and hence the scattering amplitude M, from the knowledge of the finite-volume
+spectrum. The matrices involved in the condition (14) are formally infinite-dimensional, since the
+set of possible angular momentum indices ℓ𝑚 is infinite. For practical use, we must truncate them to
+the lowest harmonics, making the approximation that K vanishes for ℓ > ℓmax. We should note that
+this relies on a fast convergence of the partial-wave expansion of the amplitude, such that keeping
+the lowest harmonics still leads to a reasonable reconstruction of the amplitude.
+4.
+The 𝑡-channel problem
+The finite-volume spectrum can sometimes include energy levels that drop below the infinite-
+volume elastic threshold at 𝑠 = (2𝑀)2. This can occur due to the appearance of a bound state (such
+that the 𝐿 → ∞ limit gives the bound-state mass) as well as to an attractive scattering state (such that
+the energy approaches 2𝑀 for 𝐿 → ∞). In many cases, the Lüscher formalism can be analytically
+continued from 𝑠 > (2𝑀)2 and the sub-threshold finite-volume energy then provides an important
+constraint on the K-matrix below threshold.
+A subtlety arises, however, when the sub-threshold two-to-two scattering amplitude M(𝑠, 𝑡), and
+therefore also the K-matrix, has a nearby 𝑡-channel cut. This is generically the case in baryon-baryon
+systems, for example, where a light meson can be exchanged in the 𝑡-channel as shown in figure 3.
+Taking 𝑚 and 𝑀 to be the meson and baryon masses, respectively, and assuming 𝑚 ≪ 𝑀, one finds
+that a pole arises in M(𝑠, 𝑡) at 𝑡 = 𝑚2. Then, for a given fixed choice of the centre-of-mass frame
+scattering angle 𝜃★, this leads to a pole in 𝑠 at
+𝑠 = 4𝑀2 −
+𝑡
+sin2(𝜃★/2)
+����
+𝑡=𝑚2 = 4𝑀2 −
+𝑚2
+sin2(𝜃★/2)
+.
+(15)
+The analytic structure of the scattering amplitude for such systems is shown in figure 4(a). From
+the expression, one sees that the pole position in 𝑠 varies from 𝑠 = 4𝑀2 − 𝑚2 to 𝑠 = −∞ as 𝜃★ is
+varied from 0 to 𝜋. As a result, the angular-momentum projection of the scattering amplitude leads
+to a branch cut running over this interval as shown in figure 4(b). Multiple meson exchanges can
+also occur, leading to additional cuts in both the fixed-𝜃★ and the angular-momentum projected
+amplitudes. In the latter case, these run along 𝑠 ≤ (2𝑀)2 − (𝑛𝑚)2 for 𝑛 exchanged mesons.
+As stressed above, finite-volume energies can arise in the region of the branch cuts (as has
+recently been identified in ref. [7]) and a naive application of the analytically continued Lüscher
+formalism fails. In this work we restrict attention to the region (2𝑀)2 − (2𝑚)2 < 𝑠 < (2𝑀)2 − 𝑚2
+in which only the single-meson cut arises and derive a modified version of the scattering formalism
+that resolves this limitation.
+7
+
+The Lüscher scattering formalism on the 𝑡-channel cut
+André Baião Raposo
+Figure 3: Meson exchanges contributing to the baryon-baryon scattering amplitude, expressed diagrammati-
+cally as a dressed 𝑡-channel meson propagator (with time flowing horizontally). The exchanged meson is a
+pion in the case of 𝑁𝑁 scattering or an 𝜂 meson in the case of ΛΛ scattering. In the latter case this is not the
+nearest singularity for physical quark masses but can become so for heavier-than-physical masses.
+Figure 4: (a) Analytic structure of the two-to-two scattering amplitude M(𝑠, 𝑡) in the complex-𝑠 plane,
+for fixed centre-of-mass scattering angle 𝜃★, in the case where a lighter particle of mass 𝑚 couples to the
+scattering particles of mass 𝑀. We show the infinite-volume elastic threshold (at 𝑠 = (2𝑀)2) and inelastic
+threshold (at 𝑠 = (2𝑀 + 𝑚)2) and corresponding branch cuts. Below threshold, we see the 𝑡-channel exchange
+pole, corresponding to 𝑡 = 𝑚2, and a lower branch cut, corresponding to two mesons being exchanged in
+the 𝑡 channel. (b) Analytic structure of the amplitude when projected to definite angular momentum. The
+so-called 𝑡-channel or left-hand cut, which runs down from the branch point at 𝑠 = (2𝑀)2 − 𝑚2, arises from
+the 𝑡-channel pole above.
+5.
+Proposed solution
+The origin of the breakdown in the original formalism can be traced back to the steps between
+eq. (7) and (10) in the review of section 3. In the step of replacing Lℓ𝑚(𝑃, |𝒌★|) and R∗
+ℓ′𝑚′(𝑃, |𝒌★|)
+with the on-shell quantities Lℓ𝑚(𝑃, 𝑘★
+os) and R∗
+ℓ′𝑚′(𝑃, 𝑘★
+os), the derivation assumes that the product
+of the two-particle pole and a given difference, e.g. Lℓ𝑚(𝑃, |𝒌★|)−Lℓ𝑚(𝑃, 𝑘★
+os), is a smooth function
+of 𝒌★. This step fails in the sub-threshold region due to the 𝑡-channel cut.
+To handle this issue, we separate out the problematic 𝑡-channel exchanges from the Bethe-Salpeter
+kernel. We define
+𝑖𝑔2𝑇(𝒌★, 𝒌′★) ≡ −𝑖𝑔2
+1
+−(𝒌★ − 𝒌′★)2 − 𝑚2 + 𝑖𝜖 ,
+(16)
+and define a modified kernel by subtracting this from the full Bethe-Salpeter kernel as shown in
+figure 5. Here, 𝑔 denotes the effective baryon-meson-baryon coupling. We emphasize that 𝑚 is the
+physical mass of the meson, and thus that −𝑖𝑇 corresponds to the singular part of the fully-dressed
+meson propagator. The difference between the bare and fully dressed propagators is smooth, and is
+simply absorbed into the modified kernel.
+8
+
+The Lüscher scattering formalism on the 𝑡-channel cut
+André Baião Raposo
+Figure 5: Separation of the standard Bethe-Salpeter kernel into a modified kernel (square box), which is safe
+to put on shell, and the problematic 𝑡-channel meson exchange, represented by a meson propagator at physical
+mass.
+Examining the modified kernel using, for instance, the cutting rules of time-ordered perturbation
+theory, shows that it can be safely evaluated at |𝒌★| = 𝑘★
+os and does not possess a singularity or cut in
+the region (2𝑀)2 − (2𝑚)2 < 𝑠 < (2𝑀)2 − 𝑚2. Crucially, we also note that the exchange 𝑖𝑔2𝑇 is safe
+if kept partially off shell, namely if we keep at least one of the magnitudes |𝒌★| and |𝒌′★| to be real.
+Recalling the expression (10) for the contribution of a skeleton expansion loop, we again
+emphasize that the finite-volume frame momentum 𝒌, and hence its centre-of-mass frame counterpart
+𝒌★, are discretized and can be indexed by 𝒏 ∈ Z3. Thus, we can then treat 𝒌★ as an extra index,
+writing L𝒌★ℓ𝑚 ≡ Lℓ𝑚(𝑃, |𝒌★|), R𝒌★ℓ𝑚 ≡ Rℓ𝑚(𝑃, |𝒌★|) and defining
+𝑆𝒌★ℓ𝑚;𝒌′★ℓ′𝑚′(𝑃; 𝐿) ≡ 1
+𝐿3 𝛿𝒌★𝒌′★Sℓ𝑚;ℓ′𝑚′(𝑃, 𝒌; 𝐿) ,
+(17)
+such that we may rewrite (10) as:
+𝐶loop
+𝐿
+(𝑃) = L𝒌★ℓ𝑚(𝑃) 𝑖𝑆𝒌★ℓ𝑚;𝒌′★ℓ′𝑚′(𝑃) R𝒌′★ℓ′𝑚′(𝑃; 𝐿) + 𝑟(𝑃) ,
+(18)
+= L(𝑃) 𝑖𝑆(𝑃; 𝐿) R(𝑃) + 𝑟(𝑃) .
+(19)
+Note that, in the first line, we are now also implicitly summing over the momentum indices. In the
+second line, we again employ a compact vector-matrix notation, but now in the angular momentum
+plus spatial loop momentum index space.
+Applying this to all loops in the skeleton expansion diagrams and rearranging by factors of
+𝑆(𝑃; 𝐿), we obtain the finite-volume correlator in the form
+𝐶𝐿(𝑃) =
+∞
+∑︁
+𝑛=0
+𝐴(𝑃) 𝑖𝑆(𝑃; 𝐿)
+�
+(𝑖 ¯𝐾 + 𝑖𝑔2𝑇(𝑃)) 𝑖𝑆(𝑃; 𝐿)
+�𝑛 𝐴†(𝑃) + 𝐶 (𝑖)
+∞ (𝑃) ,
+(20)
+where all quantities in the first term are vectors or matrices in the angular momentum plus loop
+momentum index space. Note that 𝐴(𝑃) and 𝐴†(𝑃) are different from those in (10). The matrix
+𝑖𝑔2𝑇 is the matrix of angular momentum projections of the 𝑡-channel exchange defined in (16), and
+¯𝐾(𝑃) is the sum of all possible smooth contributions one can obtain between 𝑆(𝑃; 𝐿) matrices. The
+second term 𝐶 (𝑖)
+∞ (𝑃) is a collection of 𝐿-independent terms.
+From the discussion above, we know it is safe to set |𝒌★| = 𝑘★
+os for ¯𝐾(𝑃) and, therefore,
+we can expand ¯𝐾(𝑃) about the on-shell point. We implement this by making use of a trivial
+vector 𝑢 in the momentum index space, whose elements are 𝑢𝒌★ = 1, and making the substitution
+¯𝐾(𝑃) = 𝑢 ¯K(𝑃)𝑢† +
+� ¯𝐾(𝑃) − 𝑢 ¯K(𝑃)𝑢†�. The matrix ¯K(𝑃) is a matrix in the angular momentum
+index space only and corresponds to ¯𝐾(𝑃) with the dependence on the magnitude of spatial
+momentum (through the momentum index) set to the on-shell momentum, i.e. with |𝒌★| = 𝑘★
+os. The
+9
+
+The Lüscher scattering formalism on the 𝑡-channel cut
+André Baião Raposo
+different terms in brackets lead to terms that are sums of smooth summands and can be shuffled into
+the remainder term. This yields the following expressions for the correlator:
+𝐶𝐿(𝑃) =
+∞
+∑︁
+𝑛=0
+𝐴(𝑃) 𝑖𝑆(𝑃; 𝐿)
+�
+(𝑖𝑢 ¯K(𝑃)𝑢† + 𝑖𝑔2𝑇(𝑃)) 𝑖𝑆(𝑃; 𝐿)
+�𝑛 𝐴†(𝑃) + 𝐶 (𝑖𝑖)
+∞ (𝑃) ,
+(21)
+= 𝐴(𝑃)
+𝑖
+𝑆−1(𝑃; 𝐿) + 𝑢 ¯K(𝑃)𝑢† + 𝑔2𝑇(𝑃)
+𝐴†(𝑃) + 𝐶 (𝑖𝑖)
+∞ (𝑃) .
+(22)
+Using the same arguments as in the standard derivation, we can derive a modified quantization
+condition:
+det
+�
+𝑆−1(𝐸𝑛(𝑷, 𝐿), 𝑷) + 𝑢 ¯K(𝐸𝑛(𝑷, 𝐿), 𝑷)𝑢† + 𝑔2𝑇(𝐸𝑛(𝑷, 𝐿), 𝑷)
+�
+= 0 ,
+(23)
+at all finite-volume energy levels 𝐸𝑛(𝑷, 𝐿). Given that 𝑆−1(𝐸𝑛(𝑷, 𝐿), 𝑷) and 𝑇(𝐸𝑛(𝑷, 𝐿), 𝑷) can
+be calculated numerically, one can use the knowledge of the finite-volume spectrum to obtain
+¯K(𝐸𝑛(𝑷, 𝐿), 𝑷) as well as the coupling 𝑔. This object can then be linked back to the two-to-
+two scattering amplitude via integral equations, in a similar vein to the procedure used for the
+three-particle scattering formalism refs. [22, 23, 31]. We leave further discussion to the upcoming
+paper.
+6.
+Summary & Outlook
+In this proceedings, we have described our progress in addressing issues arising in the Lüscher
+finite-volume scattering formalism [10] and extensions [11–20] in the case of sub-threshold finite-
+volume energies appearing on the 𝑡-channel cut. This work is motivated by recent lattice calculations
+in baryon-baryon systems that have observed such energy levels [7].
+To present the extension we first reviewed the standard derivation, following the method of Kim,
+Sachrajda, and Sharpe [13] for the case on non-identical spin-zero particles. We then identified
+the step in the derivation that fails to correctly account for the sub-threshold cut and provided a
+modification to address the issue. Our main result is an adapted quantization condition that applies
+above and below elastic threshold, including on the cut associated with single-meson exchange,
+though not on lower cuts arising from the exchange of multiple mesons.
+As we have in mind applications to baryon-baryon scattering, the next step, currently ongoing,
+is generalizing the derivation to particles with arbitrary intrinsic spin. Once the theoretical work is
+concluded, future directions include numerical tests on mock data (e.g. in the spirit of refs. [19, 32])
+and eventually applications to lattice QCD baryon-baryon data.
+Acknowledgements
+The authors thank Raúl Briceño, John Bulava, Evgeny Epelbaum, Drew Hanlon, Arkaitz Rodas,
+Fernando Romero-López, Maxim Mai, Steve Sharpe, and Hartmut Wittig for useful discussions
+including those in the context of the Bethe Forum on Multihadron Dynamics in a Box that took place
+at the Bethe Center for Theoretical Physics in Bonn, Germany. M.T.H. is supported by UKRI Future
+Leader Fellowship MR/T019956/1, and both M.T.H and A.B.R. are partly supported by UK STFC
+grant ST/P000630/1.
+10
+
+The Lüscher scattering formalism on the 𝑡-channel cut
+André Baião Raposo
+References
+[1] (HAL QCD), T. Inoue, S. Aoki, T. Doi, T. Hatsuda, Y. Ikeda, N. Ishii et al., Two-Baryon
+Potentials and H-Dibaryon from 3-flavor Lattice QCD Simulations, Nucl. Phys. A 881 (2012)
+28–43, [1112.5926].
+[2] E. Berkowitz, T. Kurth, A. Nicholson, B. Joo, E. Rinaldi, M. Strother et al., Two-Nucleon
+Higher Partial-Wave Scattering from Lattice QCD, Phys. Lett. B 765 (2017) 285–292,
+[1508.00886].
+[3] M. L. Wagman, F. Winter, E. Chang, Z. Davoudi, W. Detmold, K. Orginos et al.,
+Baryon-Baryon Interactions and Spin-Flavor Symmetry from Lattice Quantum
+Chromodynamics, Phys. Rev. D 96 (2017) 114510, [1706.06550].
+[4] A. Francis, J. R. Green, P. M. Junnarkar, C. Miao, T. D. Rae and H. Wittig, Lattice QCD study
+of the 𝐻 dibaryon using hexaquark and two-baryon interpolators, Phys. Rev. D 99 (2019)
+074505, [1805.03966].
+[5] (HAL QCD), T. Iritani, S. Aoki, T. Doi, T. Hatsuda, Y. Ikeda, T. Inoue et al., Consistency
+between Lüscher’s finite volume method and HAL QCD method for two-baryon systems in
+lattice QCD, JHEP 03 (2019) 007, [1812.08539].
+[6] B. Hörz et al., Two-nucleon S-wave interactions at the 𝑆𝑈(3) flavor-symmetric point with
+𝑚𝑢𝑑 ≃ 𝑚phys
+𝑠
+: A first lattice QCD calculation with the stochastic Laplacian Heaviside method,
+Phys. Rev. C 103 (2021) 014003, [2009.11825].
+[7] J. R. Green, A. D. Hanlon, P. M. Junnarkar and H. Wittig, Weakly bound 𝐻 dibaryon from
+SU(3)-flavor-symmetric QCD, Phys. Rev. Lett. 127 (2021) 242003, [2103.01054].
+[8] S. Amarasinghe, R. Baghdadi, Z. Davoudi, W. Detmold, M. Illa, A. Parreno et al., A
+variational study of two-nucleon systems with lattice QCD, 2108.10835.
+[9] Y. Lyu, H. Tong, T. Sugiura, S. Aoki, T. Doi, T. Hatsuda et al., Optimized two-baryon
+operators in lattice QCD, Phys. Rev. D 105 (2022) 074512, [2201.02782].
+[10] M. Luscher, Volume Dependence of the Energy Spectrum in Massive Quantum Field Theories.
+2. Scattering States, Commun. Math. Phys. 105 (1986) 153–188.
+[11] K. Rummukainen and S. A. Gottlieb, Resonance scattering phase shifts on a nonrest frame
+lattice, Nucl. Phys. B 450 (1995) 397–436, [hep-lat/9503028].
+[12] S. He, X. Feng and C. Liu, Two particle states and the S-matrix elements in multi-channel
+scattering, JHEP 07 (2005) 011, [hep-lat/0504019].
+[13] C. H. Kim, C. T. Sachrajda and S. R. Sharpe, Finite-volume effects for two-hadron states in
+moving frames, Nucl. Phys. B 727 (2005) 218–243, [hep-lat/0507006].
+[14] M. Lage, U.-G. Meißner and A. Rusetsky, A Method to measure the antikaon-nucleon
+scattering length in lattice QCD, Phys. Lett. B681 (2009) 439–443, [0905.0069].
+11
+
+The Lüscher scattering formalism on the 𝑡-channel cut
+André Baião Raposo
+[15] V. Bernard, M. Lage, U. G. Meißner and A. Rusetsky, Scalar mesons in a finite volume, JHEP
+01 (2011) 019, [1010.6018].
+[16] Z. Fu, Rummukainen-Gottlieb’s formula on two-particle system with different mass, Phys. Rev.
+D85 (2012) 014506, [1110.0319].
+[17] M. T. Hansen and S. R. Sharpe, Multiple-channel generalization of Lellouch-Luscher formula,
+Phys. Rev. D 86 (2012) 016007, [1204.0826].
+[18] R. A. Briceño and Z. Davoudi, Moving multichannel systems in a finite volume with
+application to proton-proton fusion, Phys. Rev. D88 (2013) 094507, [1204.1110].
+[19] P. Guo, J. Dudek, R. Edwards and A. P. Szczepaniak, Coupled-channel scattering on a torus,
+Phys. Rev. D 88 (2013) 014501, [1211.0929].
+[20] R. A. Briceño, Two-particle multichannel systems in a finite volume with arbitrary spin, Phys.
+Rev. D89 (2014) 074507, [1401.3312].
+[21] L. Meng and E. Epelbaum, Quantization conditions in the finite volume within the plane wave
+basis expansion, PoS LATTICE2021 (2022) 361.
+[22] M. T. Hansen and S. R. Sharpe, Relativistic, model-independent, three-particle quantization
+condition, Phys. Rev. D 90 (2014) 116003, [1408.5933].
+[23] M. T. Hansen and S. R. Sharpe, Expressing the three-particle finite-volume spectrum in terms
+of the three-to-three scattering amplitude, Phys. Rev. D 92 (2015) 114509, [1504.04248].
+[24] H. W. Hammer, J. Y. Pang and A. Rusetsky, Three particle quantization condition in a finite
+volume: 2. general formalism and the analysis of data, JHEP 10 (2017) 115, [1707.02176].
+[25] M. Döring, H. W. Hammer, M. Mai, J. Y. Pang, t. A. Rusetsky and J. Wu, Three-body spectrum
+in a finite volume: the role of cubic symmetry, Phys. Rev. D 97 (2018) 114508, [1802.03362].
+[26] M. Mai and M. Döring, Three-body Unitarity in the Finite Volume, Eur. Phys. J. A 53 (2017)
+240, [1709.08222].
+[27] M. Mai and M. Doring, Finite-Volume Spectrum of 𝜋+𝜋+ and 𝜋+𝜋+𝜋+ Systems, Phys. Rev. Lett.
+122 (2019) 062503, [1807.04746].
+[28] R. A. Briceño and M. T. Hansen, Multichannel 0 → 2 and 1 → 2 transition amplitudes for
+arbitrary spin particles in a finite volume, Phys. Rev. D 92 (2015) 074509, [1502.04314].
+[29] R. A. Briceño and M. T. Hansen, Relativistic, model-independent, multichannel 2 → 2
+transition amplitudes in a finite volume, Phys. Rev. D 94 (2016) 013008, [1509.08507].
+[30] R. A. Briceno, J. J. Dudek and R. D. Young, Scattering processes and resonances from lattice
+QCD, Rev. Mod. Phys. 90 (2018) 025001, [1706.06223].
+12
+
+The Lüscher scattering formalism on the 𝑡-channel cut
+André Baião Raposo
+[31] R. A. Briceño, M. T. Hansen and S. R. Sharpe, Numerical study of the relativistic three-body
+quantization condition in the isotropic approximation, Phys. Rev. D 98 (2018) 014506,
+[1803.04169].
+[32] R. A. Briceño, J. J. Dudek and L. Leskovec, Constraining 1 + J → 2 coupled-channel
+amplitudes in finite-volume, Phys. Rev. D 104 (2021) 054509, [2105.02017].
+13
+

9dE4T4oBgHgl3EQfDQsU/content/2301.04867v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2fb9efd2868bc37c46b350ac1bfc493d500429886a408e72284e719006e68316
+size 279238

9dE4T4oBgHgl3EQfDQsU/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0fa3e2fb0218e59e8c12f5aabb14ea97b6de4720987cafd6c5b9581cec5d531a
+size 147089

AtE2T4oBgHgl3EQfRQeF/content/2301.03779v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b3ec8d45db5029d28e2b7b4df284da5d45b066448e9cd8012aca82a1f4f1cd00
+size 364045

AtE2T4oBgHgl3EQfRQeF/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ec011ed714740effe3358d266f860932a78c051d1b43a3413efdce837353bd71
+size 786477

AtE2T4oBgHgl3EQfRQeF/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f721cc91a09cfeb866e065fc80e4fc94c32005bb7fb3c3ec1f4f5dd3992a409b
+size 37959

BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b7fcea1d1a97a1b86ae095d144d6fbcbd83f07281b35ae6a28a211d77ad7f00e
+size 193529

BNE1T4oBgHgl3EQfpQVQ/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3960113452c58eb4b75306660e4f73b43e742864e741db9110b440ce73c029f7
+size 2162733

BtAzT4oBgHgl3EQfwP4g/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:da97ed4206bd45bea3b7fd376d12810115cfc6b8dc8e0a55c1a5e996a6b47dec
+size 175103

CNE3T4oBgHgl3EQfUQpw/content/2301.04449v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f639744157191dae28ecf3346ced098d3313480d076fc50600f10b72f791b369
+size 1893644

CNE3T4oBgHgl3EQfUQpw/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:38e80dcc02740486d1a6b2f8909a58811bbcec501068f680c51c82e43bec74dc
+size 5308461

CtFJT4oBgHgl3EQfAiym/content/2301.11421v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4996fc0398b8a08613a4307c19af922c7f28e05923732f9bcf79498bcf15a343
+size 3221931

CtFJT4oBgHgl3EQfAiym/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5b6c2ca1b800f5bd8c42e5a69a8349423452461abda0195b5604ac9cfe51e086
+size 2490413

E9AzT4oBgHgl3EQfiv2Y/content/tmp_files/2301.01505v1.pdf.txt

@@ -0,0 +1,1036 @@
+Privacy Considerations for Risk-Based Authentication Systems
+Stephan Wiefling∗, Jan Tolsdorf, and Luigi Lo Iacono
+H-BRS University of Applied Sciences, Sankt Augustin, Germany
+∗Ruhr University Bochum, Bochum, Germany
+{stephan.wiefling,jan.tolsdorf,luigi.lo iacono}@h-brs.de
+2021 IEEE European Symposium on Security and Privacy Workshops (EuroS&PW)
+© 2022 Stephan Wiefling, Jan Tolsdorf, Luigi Lo Iacono
+Open Access version of a paper published at IWPE ’21.
+DOI: 10.1109/EuroSPW54576.2021.00040
+Abstract—Risk-based authentication (RBA) extends authen-
+tication mechanisms to make them more robust against ac-
+count takeover attacks, such as those using stolen passwords.
+RBA is recommended by NIST and NCSC to strengthen
+password-based authentication, and is already used by major
+online services. Also, users consider RBA to be more usable
+than two-factor authentication and just as secure. However,
+users currently obtain RBA’s high security and usability
+benefits at the cost of exposing potentially sensitive personal
+data (e.g., IP address or browser information). This conflicts
+with user privacy and requires to consider user rights
+regarding the processing of personal data.
+We outline potential privacy challenges regarding differ-
+ent attacker models and propose improvements to balance
+privacy in RBA systems. To estimate the properties of the
+privacy-preserving RBA enhancements in practical environ-
+ments, we evaluated a subset of them with long-term data
+from 780 users of a real-world online service. Our results
+show the potential to increase privacy in RBA solutions.
+However, it is limited to certain parameters that should guide
+RBA design to protect privacy. We outline research directions
+that need to be considered to achieve a widespread adoption
+of privacy preserving RBA with high user acceptance.
+Index Terms—Password, Risk-based Authentication, Usable
+Security and Privacy, Big Data Analysis
+1. Introduction
+Passwords are still predominant for authentication with
+online services [25], although new threats are constantly
+emerging. Credential stuffing and password spraying at-
+tacks [14] use leaked login credentials (username and
+password) sourced from data breaches, and try them
+in some way on (other) online services. These attacks
+are very popular today [2] since attackers can automate
+them with little effort. Major online services responded
+to this threat with implementing risk-based authentication
+(RBA) [36], aiming to strengthen password-based authen-
+tication with little impact on the user.
+Risk-Based Authentication (RBA). RBA determines
+whether a login attempt is a legitimate one or an account
+takeover attempt. To do so, RBA monitors additional
+features when users submit their login credentials. Popular
+features range from network (e.g., IP address), device
+This research was supported by the research training group “Human
+Centered Systems Security” (NERD.NRW) sponsored by the state of
+North Rhine-Westphalia.
+(e.g., smartphone model and operating system), or client
+(e.g., browser vendor and version), to (behavioral) biomet-
+ric information (e.g., login time) [34], [36]. Based on the
+feature values and those of previous logins, RBA calcu-
+lates a risk score. An access threshold typically classifies
+the score into low, medium, and high risk [12], [15], [21].
+On a low risk (e.g., usual device and location), the RBA
+system grants access with no further intervention. On a
+medium or higher risk (e.g., unusual device and location),
+RBA requests additional information from the user, e.g.,
+verifying the email address. After providing the correct
+proof, access is granted.
+RBA is considered a scalable interim solution when
+passwords cannot simply be replaced by more secure
+authentication methods in many cases [34], [35]. The
+National Institute of Standards and Technology (NIST,
+USA) and National Cyber Security Centre (NCSC, UK)
+recommend RBA to mitigate attacks involving stolen pass-
+words [13], [23]. Beyond that, users found RBA more
+usable than equivalent two-factor authentication (2FA)
+variants and comparably secure [35]. Also, in contrast to
+2FA, RBA both offers good security and rarely requests
+additional authentication in practice [34], reducing the
+burden on users.
+Research Questions. However, users obtain the security
+and usability gain of RBA at the cost of disclosing more
+potentially sensitive data with a personal reference, such
+as IP addresses and browser identifiers. Therefore, user
+privacy is at risk when RBA databases are forwarded
+or breached, as additional data besides usernames would
+potentially allow to identify individuals.
+More and more data protection laws aim to protect
+users from massive data collection by online services.
+Considering that, we wondered whether and to what extent
+the integration of RBA systems complies with the princi-
+ples of modern data protection. We also wondered which
+trade-offs are possible to balance security and privacy
+goals.
+To further investigate RBA’s privacy aspects, we for-
+mulated the following research questions:
+RQ1: a) In what ways can RBA features be stored to
+increase the user privacy?
+b) How can RBA features be stored to protect user
+privacy in terms of data breaches?
+RQ2: To what extent can a RBA feature maintain good
+security while preserving privacy in practice?
+Contributions. We propose and discuss five privacy en-
+hancements that can be used by RBA models used by the
+arXiv:2301.01505v1  [cs.CR]  4 Jan 2023
+
+majority of deployments found in practice. To estimate
+their usefulness in practice, we evaluated a subset of these
+enhancements on a RBA feature that is highly relevant
+in terms of security and privacy, i.e., the IP address. We
+evaluated with a data set containing the login history of
+780 users on a real-world online service for over 1.8 years.
+Our results show for the first time that it is possible to
+increase feature privacy while maintaining RBA’s security
+and usability properties. However, increasing privacy is
+limited to certain conditions that need to be considered
+while designing the RBA system. We also identified future
+challenges and research directions that might arise with a
+widespread RBA adoption in the future.
+The results support service owners to provide data pro-
+tection compliant RBA solutions. They assist developers
+in designing RBA implementations with increased privacy.
+Researchers gain insights on how RBA can become more
+privacy friendly, and further research directions.
+2. Background
+In the following section, we provide a brief introduc-
+tion to RBA and explain how the use of RBA correlates
+with the several privacy principles defined by industry
+standards and legislation.
+2.1. RBA Model
+Since RBA is not a standardized procedure, multiple
+solutions exist in practice. We focus on the implementa-
+tion by Freeman et al. [12], since it performed best in a
+previous study [34]. Also, this RBA model is known to be
+widely used, e.g., by popular online services like Amazon,
+Google, and LinkedIn [34], [36].
+The model calculates the risk score S for a user u and
+a set of feature values (FV 1, ..., FV d) with d features as:
+Su(FV ) =
+� d
+�
+k=1
+p(FV k)
+p(FV k|u, legit)
+�
+p(u|attack)
+p(u|legit)
+(1)
+S has the probabilities p(FV k) that a feature value
+appears in the global login history of all users, and
+p(FV k|u, legit) that a legitimate user has this feature
+value in its own login history. The probability p(u|attack)
+describes how likely the user is being attacked, and
+p(u|legit) describes how likely the legitimate user is
+logging in.
+2.2. Regulatory Foundations
+In the past few years, the introduction of new data
+protection laws, such as the General Data Protection Reg-
+ulation (GDPR) [8] and the California Consumer Privacy
+Act (CCPA) [30], dramatically changed the way online
+services (i.e., data controllers) process their users’ data.
+Formerly loose recommendations on handling user data
+have been replaced by clear and binding data protec-
+tion principles, which data controllers must adhere to.
+However, the details and scope of the principles vary
+between jurisdictions. For internationally operating data
+controllers, this poses the problem that their data process-
+ing operations must be designed to be compatible with
+different requirements. Fortunately, the privacy framework
+specified in ISO 29100:2011 [16] already compiles an
+intersection of privacy principles from data protection
+laws worldwide. Thus, it provides data controllers a solid
+basis for designing legally compliant data processing op-
+erations that can be tailored to the details of different
+jurisdictions. We outline the requirements for the design
+of RBA systems based on the privacy principles defined
+in ISO 29100:2011, aiming at compatibility with different
+jurisdictions.
+Applicability of Privacy Principles. Generally speaking,
+the privacy principles defined in established privacy laws
+and frameworks aim to protect the privacy of individuals.
+Thus, they only apply to data with a personal reference.
+Such data are called, e.g., “personal data” (GDPR [8]),
+“personal information” (CCPA [30]), or “personally iden-
+tifiable information” (PII) (ISO [16]). The definitions are
+very similar and usually refer to “any information that
+(a) can be used to identify [an individual] to whom such
+information relates, or (b) is or might be directly or
+indirectly linked to [an individual]” [16].
+The data processed by RBA certainly fall within this
+definition, since implementations rely on features that
+already serve as (unique) identifiers by themselves (e.g.,
+IP address) [36]. Also, the risk score calculated by RBA
+represents an identifier by itself, as it constitutes a set
+of characteristics that uniquely identifies an individual.
+Therefore, RBA has to comply with ISO 29100:2011’s
+privacy principles discussed below.
+Consent and Choice. In general, data controllers must
+ensure the lawfulness of data processing. While most
+jurisdictions recognize user consent as a lawful basis,
+applicable laws may allow processing without consent.
+Depending on the assets associated with a user account,
+data controllers may argue that RBA use is required to
+comply with the obligation to implement appropriate tech-
+nical safeguards against unauthorized access. Nonetheless,
+to ensure compliance, providers should design RBA mech-
+anisms with consent in mind and provide their users with
+clear and easy-to-understand explanations.
+Collection Limitation and Data Minimization. Data
+controllers must limit the PII collection and processing
+to what is necessary for the specified purposes. RBA
+feature sets should therefore be reviewed for suitability
+with redundant or inappropriate features removed [34].
+This includes considering using pseudonymized data for
+RBA and disposing of the feature values when they are
+no longer useful for the purpose of RBA. In practice, this
+creates the challenge to not reduce a risk score’s reliability.
+Use, Retention, and Disclosure Limitation. The data
+processing must be limited to purposes specified by the
+data controller, and data must not be disclosed to recipi-
+ents other than specified. RBA should ensure that features
+cannot be used for purposes other than the calculation
+of risk scores. Moreover, after a feature value becomes
+outdated, it should be securely destroyed or anonymized.
+We would point out that privacy laws do not apply to
+anonymized data and could therefore serve data controllers
+for developing and testing purposes beyond the retention
+period specified in their privacy statements.
+Accuracy and Quality. Data controllers must ensure that
+2
+
+the processed data are accurate and of quality. This is
+not only due to their own business interests, but also
+because data subjects have a right to expect their data
+being correct. This directly affects RBA, since it has the
+power to deny a significant benefit to users (i.e., access to
+their user account) with potentially significant harm. Data
+controllers must hence ensure by appropriate means that
+the stored feature values are correct and valid.
+Individual Participation and Access. Data controllers
+must allow data subjects to access and review their PII.
+For RBA, this means that users should be allowed to be
+provided with a copy of the feature values used.
+Information Security. Data controllers are obliged to
+protect PII with appropriate controls at the operational,
+functional, and strategic level against risks. These include,
+but are not limited to, risks associated with unauthorized
+access or processing and denial of service. Privacy laws
+demand extensive protections in this regard, “taking into
+account the state of the art, the costs of implementation
+and the nature, scope, context and purposes of processing
+as well as the risk of varying likelihood and severity for
+the rights and freedoms of natural persons” (Art. 32 (1)
+GDPR). Since RBA risk scores do not necessarily rely
+on evaluating plain text feature values [34], the collected
+data should be stored in an appropriate pseudonymized,
+masked, truncated, or encrypted form, depending on the
+RBA implementation. Moreover, data controllers should
+implement additional technical and organizational mea-
+sures as needed, and be able to ensure the integrity,
+availability, and resilience of RBA.
+Accountability and Privacy Compliance. Data con-
+trollers should inform data subjects about privacy-related
+policies, transfers of PII to other countries, and data
+breaches. Data controllers should also implement organi-
+zational measures to help them verify and demonstrate le-
+gal compliance. These include, but are not limited to, risk
+assessments and recovery procedures. RBA implementa-
+tions should therefore consider the worth of RBA features
+to both attackers and data subjects, and the recovery from
+data breaches. This is crucial in order not to undermine
+the security of user accounts and their associated assets.
+3. Privacy Enhancements (RQ1)
+To comply with the privacy principles and derived data
+protection requirements, service owners should consider
+mechanisms to increase privacy in their RBA implemen-
+tations. In the following, we introduce threats and their
+mitigation to increase privacy properties of RBA features.
+3.1. Feature Sensitivity and Impact Level
+RBA feature sets always intend to distinguish attack-
+ers from legitimate users. In doing so, the features may
+contain sensitive PII. However, not only do users per-
+ceive such PII differently regarding their sensitivity [28].
+Their (unintended) disclosure could also have far-reaching
+negative consequences for user privacy. Developers and
+providers should therefore determine the impact from a
+loss of confidentiality of the RBA feature values. Specif-
+ically, the following aspects need consideration [20]:
+Identifiability and Linkability. RBA feature sets should
+be evaluated regarding their ability to identify natural
+persons behind them. In particular, RBA systems that rely
+on intrusive online tracking methods, such as browser
+fingerprinting, store sensitive browser-specific information
+that form a linked identifier. In the event of losing confi-
+dentiality, the features would allow clear linkage between
+profiles at different online services, despite users using
+different login credentials or pseudonyms. Depending on
+the service, this could result in negative social or le-
+gal consequences for individuals. It could also enable
+more extensive and unintended activity tracking, and de-
+anonymizing information associated with user accounts.
+Previous work found that powerful RBA feature sets do
+not require to uniquely identify users when focusing on the
+detection of account takeover attempts [34]. Also, users
+are more willing to accept the processing of sensitive
+information when they are certain that it is anonymous
+and does not allow them to be identified [18], [29]. Thus,
+the use of non-intrusive features may increase user trust
+in online services, too.
+Feature Values Sensitivity. Aside from identifying in-
+dividuals by RBA feature sets, the individual feature
+values may already contain sensitive PII. Sensitive PII
+in the scope of RBA may be feature values that are
+easily spoofable and can be misused to attack other online
+services in the event of a data breach. Sensitive PII may
+also refer to data perceived as sensitive by online users.
+For example, the most important feature of current RBA
+methods, namely the IP address [12], [15], [31], [34], [36],
+is perceived as highly sensitive by online users of diverse
+cultural backgrounds [3], [19], [28]. Since users are gen-
+erally less willing to share data with increased sensitivity,
+RBA feature sets should limit the use of sensitive data if
+possible, in order to meet user interests.
+3.2. Threats
+RBA features may contain personal sensitive data,
+which has to be protected against attackers. To support
+online services in their protection efforts, we introduce
+three privacy threat types. We based the threats on those
+found in literature and our own observations in practice.
+Data Misuse. Online services could misuse their own
+RBA feature data for unintended purposes, such as user
+tracking, profiling, or advertising [5]. This type of misuse
+previously happened with phone numbers stored for 2FA
+purposes [33]. While users have to trust online services to
+not misuse their data, responsible online services should
+also take precautions to minimize chances for miuse sce-
+narios or unintended processing, e.g., by internal miscon-
+duct or after the company changed the ownership.
+Data Forwarding. Online services can be requested or
+forced to hand out stored feature data, e.g., to state actors,
+advertising networks, or other third parties. Especially
+IP addresses are commonly requested [9]. When such
+data are forwarded to third parties, the users’ privacy is
+breached. For instance, the IP address could be used to
+reveal the user’s geolocation or even their identity.
+Data Breach. Attackers obtained the database containing
+the feature values, e.g., by hacking the online service. As a
+3
+
+result, online services lost control over their data. Attack-
+ers can try to re-identify users based on the feature values,
+e.g., by combining them with other data sets. They can
+further try to reproduce the feature values and try account
+takeover attacks on a large scale, similar to credential
+stuffing. On success, they could access sensitive user data
+stored on the online service, e.g., private messages.
+3.3. Mitigation
+Online services can implement several measures to
+mitigate the outlined privacy threats. We propose five
+measures that are based on methods found in related
+research fields, as well as privacy regulations and our own
+observations with the selected RBA model (see Section 2).
+Based on the introduced RBA model, we considered all
+feature values as categorical data, in order to calculate the
+probabilities. When this condition is met, the proposed
+measures are also applicable to other RBA models [34].
+As an example for practical solutions, we describe how
+the considerations can be applied to the IP address feature,
+with regard to the IPv4 address. We chose this feature
+since it is both considered the most important RBA feature
+in terms of security to date and sensitive re-linkable data
+in terms of privacy (see Section 3.1).
+3.3.1. Aggregating. The RBA model only depends on
+feature value frequencies. To minimize data and limit
+misuse [16], we can aggregate or reorder feature data
+in the login history without affecting the results. The
+data set would then reveal how often a feature combina-
+tion occurred, but not its chronological order. Removing
+this information can mitigate re-identification in login
+sequences.
+3.3.2. Hashing. A cryptographic hash function, such as
+SHA-256, transforms a data input of arbitrary value to an
+output of fixed length. As inverting a hash function is not
+possible in theory, attackers need to recalculate all possible
+hashing values to restore the input values [17]. Assuming
+that the hashes are practically collision-free, using hashed
+feature values will produce the same RBA results as with
+the original values. This is the case, because the feature
+values are only transformed into a different representation.
+Therefore, this could be a solution to protect feature data
+in terms of the outlined threats.
+However, the IPv4 address has 32 bit limited input
+values, where some addresses have a specific semantic
+and purpose, and cannot be assigned to devices. Thus,
+attackers can simply hash all 232 − 1 values to restore the
+correct IP address. To counteract this problem, we can
+append a large random string (salt) to the input value:
+H(192.168.1.166 || salt) = 243916...aad132
+(2)
+Attackers need to guess the salt correctly, which is high
+effort when the salt is large. Thus, this mitigation strategy
+increases the required guessing time for each feature
+value. Taking it a step further, we can even hash the results
+multiple times to increase the computation time:
+H(H(...H(192.168.1.166 || salt))) = [hash]
+(3)
+This is similar to key derivation strategies used in pass-
+word databases [22]. However, we can only use a global
+salt for all database entries, as RBA mechanisms need to
+be able to identify identical feature values across users
+in the database. By increasing the computational cost,
+attackers cannot scale attacks as they would have with
+the unhashed feature values.
+3.3.3. Truncation. A more destructive approach to in-
+crease privacy for RBA features is to change or remove
+details from their data values. This can reduce the number
+of records with unique quasi identifiers. Since the feature
+data then becomes less useful for other use cases like
+tracking or re-identification, we consider it a measure to
+mitigate the privacy threats. Regarding the IP address, we
+could set the last bits to zero. For truncating the last eight
+bits, for example, this would result in:
+Truncate(192.168.1.166, 8 Bit) = 192.168.1.0
+(4)
+This mechanism is known from IP address anonymization
+strategies [6], [7]. However, we can also apply it on other
+features, e.g., reducing timing precision or coarse-graining
+browser version number in the user agent string [24].
+Since we remove information that could potentially iden-
+tify an individual, e.g., the device’s internet connection,
+this can potentially increase privacy. However, this can
+also influence the RBA results, as there are fewer feature
+values for attackers to guess.
+3.3.4. K-Anonymity.
+The k-anonymity privacy con-
+cept [32] ensures that at least k entries in a data set
+have the same quasi identifier values. If attackers obtained
+the data set and know a victim’s IP address, they would
+not be able to distinguish the person from k other users.
+This makes it an effective countermeasure against re-
+identification in case of data forwarding and data breaches.
+To achieve k-anonymity for RBA, at least k users need
+to have the same feature value. To ensure this, we added
+potentially missing entries to the RBA login history after
+each successful login. We added these entries to random
+users to only affect the global login history probabilities
+in order to keep a high security level. We created these
+users just for this purpose. To retain the global data set
+properties, the user count increased gradually to have the
+same mean number of login attempts per user.
+3.3.5. Login History Minimization. Another approach
+is to limit the login history, in terms of the amount of
+features and entries, for a number of entries or a constant
+time period [16]. A study already showed that few entries
+are sufficient to achieve a high RBA protection [34]. In so
+doing, we mitigate tracking users for an extended period
+of time. However, this can affect the RBA performance
+based on the usage pattern of the corresponding online
+service. Especially when it is a less-than-monthly-use
+online service, we assume that features need to be stored
+for a longer period than for daily use websites to achieve
+a comparable RBA performance.
+4. Case Study Evaluation (RQ2)
+Aggregating and hashing, when collision-free, does
+not affect the RBA results, as they only change the data
+representation for the RBA model. The other approaches,
+however, potentially could. To assess their impact on
+4
+
+RBA behavior in practice, we studied truncation and k-
+anonymity using real-world login data. The properties and
+limited size of our data set did not allow to reliably test
+the login history minimization approach, so we left it
+for future work. Nevertheless, we outlined this relevant
+privacy consideration for the sake of completeness. We
+used the IP address feature as in the other examples.
+4.1. Data Set
+For the evaluation, we used our long-term RBA data
+set, including features of 780 users collected on a real-
+world online service [34]. The online service collected
+the users’ features after each successful login. The users
+signed in 9555 times in total between August 2018 to
+June 2020. They mostly logged in daily (44.3%) or several
+times a week (39.2%), with a mean of 12.25 times in total.
+To improve data quality and validity, we removed all users
+who noticed an illegitimate login in their account. The
+online service was an e-learning website, which students
+used to exercise for study courses and exams. As the
+users were mostly located in the same city, it is a very
+challenging data set for RBA. They could get similar IP
+addresses with higher probability. Therefore, it is impor-
+tant to evaluate how the RBA protection changes in such
+a challenging scenario.
+4.1.1. Legal and Ethical Considerations. The study
+participants [34] signed a consent form agreeing to the
+data collection and use for study purposes. They were
+always able to view a copy of their data and delete it on
+request. The collected data were stored on encrypted hard
+drives and only the researchers had access to it.
+We do not have a formal IRB process at our university.
+Still, we made sure to minimize potential harm by com-
+plying with the ethics code of the German Sociological
+Association (DGS) and the standards of good scientific
+practice of the German Research Foundation (DFG). We
+also made sure to comply with the GDPR.
+4.1.2. Limitations. Our results are limited to the data
+set and the users who participated in the study. They
+are limited to the population of a certain region of a
+certain country. They are not representative for large-scale
+online services, but show a typical use case scenario of a
+daily to weekly use website. As in similar studies, we can
+never fully exclude that intelligent attackers targeted the
+website. However, multiple countermeasures minimized
+the possibility that the website was infiltrated [34].
+4.2. Attacker Models
+We evaluated the privacy enhancements using three
+RBA attacker models found in related literature [12], [34].
+All attackers possess the login credentials of the target.
+Naive attackers try to log in from a random Internet
+Service Providers (ISP) from somewhere in the world. We
+simulated these attackers by using IP addresses sourced
+from real-world attacks on online services [11].
+VPN attackers know the country of the victim. There-
+fore, we simulated these attackers with IP addresses from
+real-world attackers located in the victim’s country [11].
+Targeted attackers know the city, browser, and device
+of the victim. Therefore, they choose similar feature val-
+ues, including similar ISPs. We simulated these attackers
+with our data set, with the unique feature combinations
+from all users except the victim. Since the IP addresses
+of our data set were in close proximity to each other, our
+simulated attacker was aware of these circumstances and
+chose them in a similar way.
+4.3. Methodology
+In order to test our privacy enhancements in terms
+of practical RBA solutions, we defined a set of desired
+properties. Our enhancements need to: (A) Keep the
+percentage of blocked attackers: The ability to block a
+high number of attackers should not decrease when using
+the privacy enhancements. This is necessary to keep the
+security properties of the RBA system. (B) Retain differ-
+entiation between legitimate users and attackers: When
+applied, the risk score differences between legitimate users
+and attackers should only change within a very small
+range. Otherwise, the usability and security properties of
+the RBA system would decrease.
+We outline the tests to evaluate the privacy enhance-
+ments below. Based on the method in Wiefling et al. [34],
+we reproduced the login behavior for attackers and legit-
+imate users by replaying the user sessions. We integrated
+truncation and k-anonymity in the reproduction process,
+to test the countermeasures.
+The RBA model used the IP address and user agent
+string as features, since this can be considered the RBA
+state of practice [34], [36]. We truncated the IP addresses
+in ranges from 0 to 24 bits, to observe the effects on
+the RBA performance. We assume that cutting more than
+25 bits will not allow to reliably detect attackers. We also
+tested k-anonymity with the IP address feature until k = 6.
+As US government agencies consider less than five entries
+to be sensitive [10], we chose to cover this threshold.
+4.3.1. Test A: Percentage of Blocked Attackers. To
+compare the RBA performance regarding all three attacker
+models, we calculated the percentage of how many attack-
+ers would be blocked. We call this percentage the true
+positive rate (TPR), as previous work did [12], [34]. For
+a fair comparison, we observed how the TPR changed
+when aiming to block 99.5% of attackers. We chose this
+TPR baseline since it showed good performance regarding
+usability and security properties in a previous study [34].
+To ease comparison, we adjusted the TPR for each
+truncation or k-anonymity step xi as percentage differ-
+ences to the baseline without modifications (relative TPR):
+TPRrelativexi = TPRxi − TPRbaseline
+TPRbaseline
+(5)
+Following that, TPRrelativexi < 0.0 means that the TPR
+decreased compared to the baseline.
+4.3.2. Test B: Risk Score Changes. To determine the
+degree that attackers and legitimate users can be differ-
+entiated in the RBA model, we calculated the risk score
+relation (RSR) [34]. It is the relation between the mean
+risk scores for attackers and legitimate users:
+RSRbasic =
+mean attacker risk score
+mean legitimate risk score
+(6)
+5
+
+To ease comparison, we normalized each RSR for every
+truncation or k-anonymity step xi as percentage differ-
+ences to the baseline (relative RSR). The baseline is the
+IP address without modifications:
+RSRrelativexi =
+RSRbasicxi − RSRbaseline
+RSRbaseline
+(7)
+As a result, RSRrelativexi < 0.0 signals that attackers and
+legitimate users can no longer be distinguished as good
+as they were before introducing the privacy enhancing
+measures.
+4.3.3. Limit Extraction. For each test, we defined the
+following thresholds to extract limits that do not degrade
+RBA performance to an acceptable extent.
+(Test A) We require the RBA performance to remain
+constant. Thus, we selected the reasonable limit as the
+point at which the relative TPR decreases compared to
+the baseline, i.e., attackers cannot be blocked as good
+as before any more. (Test B) Unlike tracking, RBA uses
+the feature information in addition to an already verified
+identifier, e.g., passwords. Thus, we consider it feasible
+to reduce the RSR slightly for the sake of privacy. Based
+on our observations, RSR changes below 0.01 can be
+tolerable for our case study evaluation. Thus, we chose
+the reasonable limit as the point at which the relative RSR
+is lower than 0.01.
+4.4. Results
+In the following, we present the results for all attacker
+models. We discuss the results after this section. We used
+a high performance computing cluster using more than
+2000 cores for the evaluation. This was necessary since
+calculating the results with the simulated attackers was
+computationally intensive.
+For statistical testing, we used Kruskal-Wallis tests
+for the omnibus cases and Dunn’s multiple comparison
+test with Bonferroni correction for post-hoc analysis. We
+considered p-values less than 0.05 to be significant.
+4.4.1. Truncation. Figure 1 shows the truncation test
+results for all attackers. The TPR differences between
+the targeted attacker and both remaining attackers were
+significant
+(Targeted/Naive:
+p=0.0151,
+Targeted/VPN:
+p<0.0001). The TPRs exceeded the limit after 20 bits for
+naive, 3 bits for VPN, and 14 bits for targeted attackers.
+Regarding the relative RSRs, there are significant
+differences between VPN and both remaining attackers
+(p<0.0001). The RSRs exceeded the limit after 3 bits for
+naive, 21 bits for VPN, and 3 bits for targeted attackers.
+Combining both results, the accepted truncation limits
+based on our criteria were 3 bits for all attacker models.
+4.4.2. K-Anonymity. Figure 2 shows the combined k-
+anonymity test results for the three attacker models. The
+relative TPR decreased after k = 1 for targeted attack-
+ers, k = 2 for naive attackers, and not at all for VPN
+attackers until at least k = 6. There were significant TPR
+differences between naive and VPN attackers (p=0.0066).
+The relative RSR did not decrease for all attacker types
+and there were no significant differences.
+0.0010
+0.0005
+0.0000
+0.0005
+0.0010
+0.0015
+Relative TPR
+Attacker
+Targeted
+VPN
+Naive
+0
+2
+4
+6
+8
+10 12 14 16 18 20 22 24
+Truncated IP Address Bits
+0.3
+0.2
+0.1
+0.0
+0.1
+0.2
+Relative Risk
+ Score Relation
+Attacker
+Targeted
+VPN
+Naive
+Figure 1. Results for truncating the IP address. Top: Relative TPR (Test
+A). There were significant differences between targeted and both VPN
+and naive attackers. Bottom: Relative RSR (Test B). The differences
+between VPN and both targeted and naive attackers were significant.
+0.0010
+0.0005
+0.0000
+0.0005
+0.0010
+0.0015
+Relative TPR
+Attacker
+Targeted
+VPN
+Naive
+1
+2
+3
+4
+5
+6
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+Relative Risk
+ Score Relation
+Attacker
+Targeted
+VPN
+Naive
+Figure 2. Results for k-anonymity regarding the IP address. Top: Relative
+TPR (Test A). Differences between naive and VPN attackers were
+significant. Bottom: Relative RSR (Test B). There were no significant
+differences.
+Combining the results, the acceptable k levels based
+on our criteria were k = 1 for targeted attackers, k = 2
+for naive attackers, and at least k = 6 for VPN attackers.
+5. Discussion
+Our results show that IP address truncation signifi-
+cantly affects the RBA risk score and reduces the proba-
+bility of attack detection. The truncation for VPN attackers
+resulted in a local maximum of the RSR at 12 bits, and
+thus apparently improved detection. However, this was due
+to the fact that the VPN attacker only had an IP address
+range limited to the VPN service’s server locations. Since
+the first IP address bits correspond to a node’s geolocation,
+they were mostly distinct from legitimate users residing in
+different areas. Thus, truncating increased the risk scores
+for VPN attackers until 12 bit, as the probability for the
+global login history p(FV k) decreased but the one for
+the local history p(FV k|u, legit) remained constant. In
+contrast to that, targeted attackers also had a limited IP
+address range, but they were located in the same region as
+the legitimate users. Also, naive attackers had a large IP
+address range. Thus, in both cases, the differences between
+p(FV k) and p(FV k|u, legit) remained constant to similar
+levels until 12 bits.
+Following that, and what our evaluation indicates, we
+6
+
+TABLE 1. OVERHEAD CREATED BY ADDITIONAL LOGIN ENTRIES TO
+ACHIEVE K-ANONYMITY
+k
+Additional Entries
+Increase to Baseline
+1
+0
+0.0
+2
+3928
+0.41
+3
+7965
+0.83
+4
+12013
+1.26
+5
+16065
+1.68
+6
+20120
+2.11
+do not recommend truncating more than three bits for a
+stable RBA performance in our case study scenario.
+K-anonymity increased the distinguishability between
+legitimate users and attackers, i.e., the RSR. This was
+due to the fact that this mechanism added new entries
+to the global login history. As a result, the overall prob-
+ability for unknown feature values in the global login
+history p(FV k) decreased, making it harder for attackers
+to achieve a low risk score. However, this also decreased
+the detection of attackers, i.e., the TPR, in most cases,
+since k more users had similar feature values in the data
+set. As a side effect of these results, unique feature values
+got less unique in total. Thus, due to the determined limit
+of k = 1, k-anonymity for targeted attackers can only be
+achieved with degraded RBA performance.
+The overhead produced by the additional entries in-
+creased with each k (see Table 1). It was even more
+than the data set itself at k>3, which makes the current
+mechanism impractical for very large online services. To
+mitigate this issue, mechanisms could be introduced which
+remove some additional login entries when k-anonymity
+can be fulfilled after some time.
+K-anonymity is not scalable with an increasing num-
+ber of features [1], while the other approaches are. Thus,
+sensible RBA privacy enhancements might be a combina-
+tion of all outlined countermeasures, to ensure scalability.
+Based on our results, we discuss privacy challenges
+and further research directions in the following.
+5.1. Privacy Challenges
+When integrating privacy into RBA systems, there are
+several challenges that should be considered in practice.
+We describe them below.
+Role of the IP Address Feature. Using a combination
+of privacy enhancements for the IP address might be
+sufficient for some applications. However, this feature
+is still sensitive information. Thus, the question arises
+whether online services should consider privacy enhancing
+alternatives instead of storing the IP address. One alterna-
+tive could be to derive only the region and ASN from the
+IP address, and discard the rest. Other approaches even
+enable identifying network anomalies, e.g., IP spoofing
+using a VPN connection, without having to rely on the IP
+address at all. For example, the server-originated round-
+trip time (RTT) [34] can be used to estimate the distance
+between the user’s device and the server location and may
+replace IP addresses as RBA features. As the RTTs vary
+based on the server location, they become useless for most
+re-identification attacks using leaked databases, as server
+locations are distributed in practice. They can even be
+enriched with random noise to further enhance privacy.
+Risk of Feature Stuffing. Such considerations can be
+more and more important with widespread RBA adop-
+tion in the future. We assume that when databases with
+RBA feature values got stolen, this might have serious
+consequences for other services using RBA. In contrast
+to passwords, behavioral RBA feature values cannot be
+changed after compromise. Attackers can attempt to auto-
+matically reproduce these feature values on other websites.
+Thus, more privacy preserving alternatives that are hard
+to spoof for attackers might be crucial to mitigate largely
+scalable “feature stuffing” attacks.
+Handling Data Deletion Requests. Further conflicts
+could arise with data protection regulations. Users are
+legally permitted to request data deletion. So when they
+request online services to delete their RBA feature data,
+they might lose RBA protection on their user accounts.
+5.2. Research Directions
+Our case study evaluation provided first insights on
+truncating feature values to increase privacy. As the results
+showed that this is possible to a certain degree while main-
+taining RBA performance, further work can investigate it
+for other types of features, e.g., the user agent string.
+The proposed k-anonymity mechanism can increase
+privacy regarding unique entries in the data set. However,
+users might still be identifiable when they have a combi-
+nation of typical feature values, e.g., a home and a work
+IP address. This non-trivial task had been addressed in
+dynamic databases [27], [37]. Future work may investigate
+whether such mechanisms are also applicable to RBA.
+As we could not reliably test the login history mini-
+mization approach with our data set, future work should
+investigate this on a medium to large-scale online service
+with regular use.
+6. Related Work
+Burkhard et al. [6] investigated truncating IP addresses
+in anomaly detection systems. They found that truncating
+more than four bits degraded the performance of these
+systems. Chew et al. [7] further evaluated IP truncation
+in intrusion detection systems. Their results showed that
+the detection accuracy in many of the tested classifiers
+decreased after removing more than 8 bits. Our study
+showed that three bits could be removed from the IP
+address to maintain RBA performance at the same time.
+Both Safa et al. [26], and Blanco-Justicia and
+Domingo-Ferrer [4] proposed privacy-preserving authen-
+tication models for implicit authentication using mobile
+devices. Their models relied on client-originated features,
+and the former also calculated risk scores on the client’s
+device. However, this is not applicable to our RBA use
+case, as it relies on server-originated features and risk
+scores to prevent client-side spoofing.
+To the best of our knowledge, there were no studies in-
+vestigating privacy enhancements in RBA systems. How-
+ever, some literature touched on privacy aspects related
+to RBA. Bonneau et al. [5] discussed privacy concerns of
+using additional features for authentication. They found
+that privacy preserving techniques might mitigate these
+concerns, but these had not been deployed in practice. We
+7
+
+proposed and tested some techniques for the first time in
+our case study. Wiefling et al. [35] investigated RBA’s
+usability and security perceptions. The results showed
+that users tended to reject providing phone numbers to
+online services for privacy reasons. They further studied
+RBA characteristics on a real-world online service [34],
+showing that the feature set can be very small to achieve
+good RBA performance. We demonstrated that the privacy
+can be further enhanced through different mechanisms.
+7. Conclusion
+With a widespread use of RBA to protect users against
+attacks involving stolen credentials, more and more online
+services will potentially store sensitive feature data of their
+users, like IP addresses and browser identifiers, for long
+periods of time. Whenever such information is forwarded
+or leaked, it poses a potential threat to user privacy. To
+mitigate such threats, the design of RBA systems must
+balance security and privacy.
+Our study results provide a first indication that RBA
+implementations used in current practice can be designed
+to become more privacy friendly. However, there are still
+challenges that have not been resolved in research to
+date. An important question is, e.g., how the IP address
+feature can be replaced with more privacy preserving
+alternatives. On the one hand, we assume that the IP
+address is very relevant for re-identification attacks [9].
+Discarding it from the RBA login history can therefore
+increase privacy protection. On the other hand, the IP
+address is a feature providing strong security [34]. Future
+research must carefully identify and analyze such trade-
+offs, so that RBA’s user acceptance does not drop with
+the first data breach.
+References
+[1]
+C. C. Aggarwal, “On k-Anonymity and the Curse of Dimension-
+ality,” in VLDB ’05.
+VLDB Endowment, Aug. 2005.
+[2]
+Akamai, “Loyalty for Sale – Retail and Hospitality Fraud,” [state
+of the internet] / security, vol. 6, no. 3, Oct. 2020.
+[3]
+K. Almotairi and B. Bataineh, “Perception of Information Sensi-
+tivity for Internet Users in Saudi Arabia,” AIP, vol. 9, no. 2, 2020.
+[4]
+A. Blanco-Justicia and J. Domingo-Ferrer, “Efficient privacy-
+preserving implicit authentication,” Computer Communications,
+vol. 125, Jul. 2018.
+[5]
+J. Bonneau, E. W. Felten, P. Mittal, and A. Narayanan, “Privacy
+concerns of implicit secondary factors for web authentication,” in
+WAY ’14, Jul. 2014.
+[6]
+M. Burkhart, D. Brauckhoff, M. May, and E. Boschi, “The risk-
+utility tradeoff for IP address truncation,” in NDA ’08.
+ACM,
+2008.
+[7]
+Y. J. Chew, S. Y. Ooi, K.-S. Wong, and Y. H. Pang, “Privacy
+Preserving of IP Address through Truncation Method in Network-
+based Intrusion Detection System,” in ICSCA ’19.
+ACM, 2019.
+[8]
+European Union, “General Data Protection Regulation,” May 2016,
+Regulation (EU) 2016/679.
+[9]
+Europol, “SIRIUS EU Digital Evidence Situation Report 2019,”
+Dec. 2019.
+[10] Federal Committee on Statistical Methodology, “Report on Statis-
+tical Disclosure,” Dec. 2005.
+[11] FireHOL,
+“All
+cybercrime
+ip
+feeds,”
+Aug.
+2020.
+[Online].
+Available: http://iplists.firehol.org/?ipset=firehol level4
+[12] D. Freeman, S. Jain, M. D¨urmuth, B. Biggio, and G. Giacinto,
+“Who Are You? A Statistical Approach to Measuring User Au-
+thenticity,” in NDSS ’16.
+Internet Society, Feb. 2016.
+[13] P. A. Grassi et al., “Digital identity guidelines: authentication
+and lifecycle management,” National Institute of Standards and
+Technology, Tech. Rep. NIST SP 800-63b, Jun. 2017.
+[14] M. J. Haber, “Attack Vectors,” in Privileged Attack Vectors: Build-
+ing Effective Cyber-Defense Strategies to Protect Organizations.
+Apress, 2020.
+[15] A. Hurkała and J. Hurkała, “Architecture of context-risk-aware
+authentication system for web environments,” in ICIEIS ’14, 2014.
+[16] ISO, ISO/IEC 29100:2011(E): Information Technology — Security
+Techniques — Privacy Framework.
+ISO/IEC, 2011.
+[17] D. Llewellyn-Jones and G. Rymer, “Cracking PwdHash: A Brute-
+force Attack on Client-side Password Hashing.”
+Apollo, 2017.
+[18] E. Markos, L. I. Labrecque, and G. R. Milne, “A New Information
+Lens: The Self-concept and Exchange Context as a Means to
+Understand Information Sensitivity of Anonymous and Personal
+Identifying Information,” JIM, vol. 42, 2018.
+[19] E. Markos, G. R. Milne, and J. W. Peltier, “Information Sensitivity
+and Willingness to Provide Continua: A Comparative Privacy Study
+of the United States and Brazil,” JPP&M, 2017.
+[20] E. McCallister, T. Grance, and K. A. Scarfone, “Guide to protecting
+the confidentiality of Personally Identifiable Information (PII),”
+Tech. Rep. NIST SP 800-122, 2010.
+[21] I. Molloy, L. Dickens, C. Morisset, P.-C. Cheng, J. Lobo, and
+A. Russo, “Risk-based Security Decisions Under Uncertainty,” in
+CODASPY ’12.
+ACM, Feb. 2012.
+[22] K. Moriarty, B. Kaliski, and A. Rusch, “Pkcs #5: Password-based
+cryptography specification version 2.1,” RFC 8018, January 2017.
+[23] National Cyber Security Centre, “Cloud security guidance: 10,
+Identity and authentication,” Tech. Rep., Nov. 2018.
+[24] G. Pugliese, C. Riess, F. Gassmann, and Z. Benenson, “Long-Term
+Observation on Browser Fingerprinting: Users’ Trackability and
+Perspective,” PoPETS, vol. 2020, no. 2, Apr. 2020.
+[25] N. Quermann, M. Harbach, and M. D¨urmuth, “The State of User
+Authentication in the Wild,” in WAY ’18, Aug. 2018.
+[26] N. A. Safa, R. Safavi-Naini, and S. F. Shahandashti, “Privacy-
+Preserving Implicit Authentication,” in IFIP SEC ’14.
+Springer,
+2014.
+[27] J. Salas and V. Torra, “A General Algorithm for k-anonymity on
+Dynamic Databases,” in DPM ’18.
+Springer, 2018.
+[28] E.-M. Schomakers, C. Lidynia, D. M¨ullmann, and M. Ziefle,
+“Internet users’ perceptions of information sensitivity – insights
+from Germany,” IJIM, vol. 46, Jun. 2019.
+[29] E.-M. Schomakers, C. Lidynia, and M. Ziefle, “All of me? Users’
+preferences for privacy-preserving data markets and the importance
+of anonymity,” Electronic Markets, vol. 30, no. 3, Feb. 2020.
+[30] State of California, “California Consumer Privacy Act,” Jun. 2018,
+Assembly Bill No. 375.
+[31] R. H. Steinegger, D. Deckers, P. Giessler, and S. Abeck, “Risk-
+based authenticator for web applications,” in EuroPlop ’16. ACM,
+Jun. 2016.
+[32] L. Sweeney, “k-anonymity: A model for protecting privacy,”
+IJUFKS, vol. 10, no. 05, Oct. 2002.
+[33] G. Venkatadri, E. Lucherini, P. Sapiezynski, and A. Mislove, “In-
+vestigating sources of PII used in Facebook’s targeted advertising,”
+PoPETS, vol. 2019, Jan. 2019.
+[34] S. Wiefling, M. D¨urmuth, and L. Lo Iacono, “What’s in Score
+for Website Users: A Data-driven Long-term Study on Risk-based
+Authentication Characteristics,” in FC ’21.
+Springer, Mar. 2021.
+[35] S. Wiefling, M. D¨urmuth, and L. Lo Iacono, “More Than Just
+Good Passwords? A Study on Usability and Security Perceptions
+of Risk-based Authentication,” in ACSAC ’20.
+ACM, Dec. 2020.
+[36] S. Wiefling, L. Lo Iacono, and M. D¨urmuth, “Is This Really You?
+An Empirical Study on Risk-Based Authentication Applied in the
+Wild,” in IFIP SEC ’19.
+Springer, Jun. 2019.
+[37] X. Xiao and Y. Tao, “M-invariance: towards privacy preserving re-
+publication of dynamic datasets,” in SIGMOD ’07.
+ACM, 2007.
+8
+

EtE0T4oBgHgl3EQfgwHQ/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:81e48d057ddff13a6d3ddef3c62ec5d7a7869a967dd183d4316157360cf4581a
+size 262721

G9FAT4oBgHgl3EQfth4f/content/tmp_files/2301.08664v1.pdf.txt

@@ -0,0 +1,1252 @@
+AccDecoder: Accelerated Decoding for
+Neural-enhanced Video Analytics
+Tingting Yuan†§, Liang Mi‡§, Weijun Wang†‡, Haipeng Dai‡∗, Xiaoming Fu†
+†University of G¨ottingen, Germany; ‡Nanjing University, China
+{tingting.yuan,weijun.wang,fu}@cs.uni-goettingen.de, [email protected], [email protected]
+Abstract—The quality of the video stream is key to neural
+network-based video analytics. However, low-quality video is
+inevitably collected by existing surveillance systems because of
+poor quality cameras or over-compressed/pruned video streaming
+protocols, e.g., as a result of upstream bandwidth limit. To ad-
+dress this issue, existing studies use quality enhancers (e.g., neural
+super-resolution) to improve the quality of videos (e.g., resolution)
+and eventually ensure inference accuracy. Nevertheless, directly
+applying quality enhancers does not work in practice because
+it will introduce unacceptable latency. In this paper, we present
+AccDecoder, a novel accelerated decoder for real-time and neural-
+enhanced video analytics. AccDecoder can select a few frames
+adaptively via Deep Reinforcement Learning (DRL) to enhance
+the quality by neural super-resolution and then up-scale the
+unselected frames that reference them, which leads to 6-21%
+accuracy improvement. AccDecoder provides efficient inference
+capability via filtering important frames using DRL for DNN-
+based inference and reusing the results for the other frames via
+extracting the reference relationship among frames and blocks,
+which results in a latency reduction of 20-80% than baselines.
+Index Terms—Video analytics, super-resolution, deep rein-
+forcement learning
+I. INTRODUCTION
+Advances in computer vision offer tremendous opportunities
+for autonomous analytics of videos generated by pervasive
+video cameras. Deep Neural Networks (DNNs) [1]–[4] have
+been developed to dramatically improve the accuracy for
+various vision tasks, while introducing stringent demands
+on computational resources. Due to the compute-resource
+shortage of commercial cameras, videos need to be streamed
+to powerful servers for inference, which is called distributed
+video analytics pipeline (VAP) [5], [6].
+Nevertheless, providing highly accurate video analytics re-
+mains challenging for the state-of-the-art distributed VAPs.
+Since most methods for video analytics currently rely on high-
+resolution videos, it is difficult to analyze low-quality videos,
+such as object detection at low resolutions. For example, the
+accuracy of Faster R-CNN [3], a modern DNN-based inference
+method, can only achieve around 56% accuracy for videos
+in 360p and 61% accuracy for videos in 540p which are
+collected by [7]. However, low-quality videos are inevitably
+collected by existing surveillance systems. One of the reasons
+is that existing low-quality collectors can only capture low-
+resolution frames. For example, New York city’s department
+of transportation [8] has made videos from all 752 traffic
+cameras to the public; however, the videos are transmitted
+*Corresponding author. §Equal contributors.
+at an extremely low resolution (240p) due to the default
+configuration of cameras [9]. Another reason is that current
+video streaming protocols over-compress/prune videos due to
+upstream bandwidth limitations. For example, AWStream [10]
+aggressively reduces the resolution of the video from 540p to
+360p and the frame rate from 1 to 0.83. It eventually brings
+about a 66% saving of bandwidth with a reduced accuracy
+from 61% to 54%.
+To address this challenge, some VAPs [11], [12] try to
+utilize image enhancement models like Super Resolution (SR)
+[2], [13] and Generative Adversarial Network (GAN) [14]
+to enhance frames in videos before feeding them into the
+inference model. This idea is inspired by the observation from
+the computer vision community – running object recognition-
+related tasks on high-resolution images can largely improve
+the detection accuracy [13]. However, the video enhancement
+via DNN-aware image enhancement models introduces extra
+latency, resulting in around 500 ms end-to-end latency [15]
+for each frame, which is far from the real-time requirement
+(e.g., less than 15-30 ms for real-time object recognition [6]).
+Although existing DNN-aware video enhancement provides
+a promising way to improve the inference accuracy [16],
+there is still much room for improvement. First, prior video
+enhancement mechanisms are largely agnostic to video con-
+tents, treating each received frame equally, but not all the
+frames need to be enhanced. For example, only the frames
+containing vehicles are valuable for traffic flow analysis; on
+the contrary, enhancing frames with empty streets is worthless
+but only increases system latency. Therefore, content-agnostic
+enhancement mechanisms cannot avoid being suboptimal.
+Second, although new DNN frameworks are designed to
+accurately recognize important frames (e.g., [17], [18]), they
+are too heavy to achieve low latency. Third, decoding all the
+frames for analytics is computationally intensive and time-
+consuming, and video encoding contains plenty of unexploited
+but handy information to capture the important frames, such as
+motion vectors (MVs) and residuals. We argue that the codec
+information, although inaccurate, is valuable to reveal which
+content is important, thereby speeding up video analytics.
+Motivated by the above insights, we present AccDecoder,
+a novel accelerated video streaming decoder for real-time and
+neural-enhanced video analytics. AccDecoder is a content-
+aware DNN-integrated video decoder utilizing codec informa-
+tion to select a few frames for quality enhancement, which
+is called as anchor frames and some frames for DNN-aware
+arXiv:2301.08664v1  [cs.CV]  20 Jan 2023
+
+0.2
+0.4
+0.6
+0.8
+F1-score
+0
+15
+30
+45
+FPS
+AccDec.
+DDS
+Reducto
+Glimpse
+AWStream
+Better
+Fig. 1: Example results of AccDecoder vs. baselines.
+inference, which is called as inference frames. In particular,
+AccDecoder applies SR to anchor frames and transfers the
+high quality of frames/blocks to benefit the entire video via
+extracting the frame and block reference relationships; it
+further leverages codec information to reuse the results of
+inference frames for acceleration.
+Challenge and solution. AccDecoder needs to adapt to
+various quality of videos to enable robust and real-time
+video analytics. Since SR and DNN-based inference is time-
+consuming, an accuracy-latency tradeoff must be made care-
+fully to keep low latency without drastically compromising the
+accuracy. Our preliminary study (see more in Section II and
+III) shows that AccDecoder needs adaptive metrics for anchor
+and inference frame selection according to factors like video
+content and quality. In other words, various videos (or even
+different chunks of the same video) demand different settings
+for frame selection, but a static setting is not adaptive to the
+varying contents of videos. To address this issue, we leverage
+deep reinforcement learning (DRL) [19]–[21], which has been
+widely used to solve dynamic and sequential problems [22],
+[23]. Specifically, AccDecode enables adaptive settings via
+DRL in frame selection to accelerate the video analytics and
+achieve a good tradeoff between accuracy and latency.
+Our contributions are summarized as follows.
+• We design a novel content-aware DNN integrated video
+decoder that is resilient and robust to the quality of videos.
+For example, for a 540p crossroad video collected by [7],
+AccDecoder can improve 10-38% accuracy compared with
+the state-of-the-art VAPs (see Fig. 1).
+• We exploit temporal redundancies within a video and codec
+information to drastically increase the speed of analytics.
+For example, AccDecoder performs 1.5-8.0 times faster
+compared with AWStream [10], DDS [5], and Glimpse [24]
+(see Fig. 1).
+The rest of the paper is organized as follows. We first
+present the background and motivation in Section II. Then we
+discuss AccDecoder’s key design in Section III, followed by
+our implementation in Section IV. The experimental studies
+are demonstrated in Section V. In Section VI, we introduce
+some related work. We conclude this paper in Section VII.
+II. BACKGROUND AND MOTIVATION
+We introduce distributed VAPs and video codec, followed
+by performance requirements of VAPs that drive our design
+(i.e., high accuracy, low end-to-end latency, and low over-
+heads). We then elaborate on why prior solutions struggle to
+meet the three requirements simultaneously.
+A. Background
+Distributed Video Analytics. The proliferation of video an-
+alytics is facilitated by the advances of deep learning and
+the low prices of high-resolution network-connected cam-
+eras. However, the accuracy improvement from deep learning
+comes at a high computational cost. Although state-of-the-
+art smart cameras can support deep learning methods, the
+current surveillance and traffic cameras show only suboptimal
+use of resources. For example, DNNCam [25] that ships with
+a high-end embedded NVIDIA TX2 GPU [26] costs more
+than $2000 while the price of deployed traffic cameras today
+ranges $40-$200. These cameras are typically loaded with a
+single-core CPU, only providing scarce compute resources.
+Because of this huge gap, typical VAPs follow a distributed
+architecture. A typical distributed VAP architecture includes a
+filter and an encoder on the camera side and a decoder and
+an inference model on the server side, as illustrated in Fig.
+2. In live analytics, video frames are continuously encoded
+and sent to a remote server that runs the inference DNN to
+analyze the video in an online fashion. For example, a vehicle
+detection pipeline consists of a front-end traffic camera (which
+compresses and streams live videos to a compute-powerful
+edge/cloud GPU server upon wire/wireless networks) and a
+back-end server (which decodes received video into frames
+and feeds them into inference models like Faster R-CNN [3]
+to detect vehicles). Such an architecture brings challenges in
+bandwidth cost, and thus some schemes rely on aggressively
+pruning videos (via e.g., reconfiguration, filtering) to meet
+upstream bandwidth limitations.
+frames
+bits
+stream
+feedback
+Server
+frames
+inference
+results
+decoder
+encoder
+filter
+Camera
+Fig. 2: Distributed video analytics pipeline.
+Video codec is the key technology in distributed VAPs. It
+comprises an encoder and a decoder, a software/hardware
+program used to compress/decompress video files for easier
+storage or network delivery. The encoder compresses video
+data and wraps them into common video formats (e.g., H.264
+[27]), while the decoder decompresses the compressed video
+data into frames before post-processing (e.g., playback or
+analysis). This compression process is usually lossy, which
+strikes a balance between the video quality and the com-
+pression ratio according to the self-preference of codecs and
+encoding settings of users (e.g., bitrate, frame rate, and group
+of pictures). We take H.264, one of the most popular codecs,
+as an example to explain the compression process. During
+encoding, each video frame is first divided into non-overlapped
+macroblocks (16×16 pixels), then to each macroblock, the
+
+encoder searches for the optimal compression method (in-
+cluding the block division types and encoding types of each
+block) according to the pixel-level similarity and encoding
+settings. One macroblock may be further divided into non-
+overlapped blocks (8×8 or 8×16 pixels) encoded with intra-
+or inter-frame types. The intra-coded block is encoded using
+the reference block with the most pixel-value similarity, and
+the offset between these two blocks is encoded into an MV
+with a residual. With the same procedure, the inter-coded
+block locates the most pixel-value similar block searched by
+the reference index and the MV from other frames. An MV
+indicates the spatial offset between the target block and its
+reference, while the difference in pixel values of two blocks
+is encoded as the residual for decoding.
+An ideal distributed VAP should meet three goals:
+• High accuracy. Inspired by the success of image enhance-
+ment methods in video streaming for QoE improvement
+[28]–[31], researchers try to use image enhancement for
+machine-centric video analytics [15], [31], [32]. For ex-
+ample, [15] leverages SR to enhance image details for
+robotics applications, while [31] embeds GAN on Google
+Glasses to generate facial features for face recognition. The
+experimental results from [15], [31] demonstrate that image
+enhancement improves inference accuracy.
+• Low latency. The latency of decoding the video (i.e.,
+decoding latency), inference, and streaming the video to
+the server (i.e., streaming latency) should be low. Previous
+works focus on reducing the size of streaming to reduce the
+streaming latency (e.g., Reducto [3]), learning and filtering
+key frames for inference, and utilizing MVs to reuse the
+other frames.
+• Low bandwidth cost. We define the total size of a video
+file delivered from the camera to the server of each VAP as
+its bandwidth cost.
+B. Motivation
+Limitations
+of
+previous
+work. Although a couple of
+bandwidth-saving and accuracy-improvement approaches have
+been developed, three significant limitations remain.
+• Adaptive encoding in cameras. A camera may leverage
+light-weight DNN [33] or heuristic methods (e.g., inter-
+frame pixel-level difference [24]) to distinguish and prune
+frames/regions without labelled information. However, these
+cheap methods may cause false positive (e.g., pixel-level
+distance changes by background may trigger a camera to
+send many frames) and false negative (e.g., cheap object
+detection model may miss small appeared objects), thus in-
+creasing bandwidth cost or reducing the inference accuracy.
+Server-side decision-making controls the camera’s actions
+with feedback from the cloud. For example, according to
+the servers’ instruction, the camera in [5] iteratively delivers
+the region of interest in a higher resolution. The server-side
+decision-making introduces extra latency, especially due to
+the information delivery between the camera and the cloud
+crossing a wide area network.
+• Image enhancement in servers. Image enhancement con-
+tributes to higher accuracy but also causes higher latency.
+Although recent studies have successfully leveraged image
+enhancement to increase QoE and inference accuracy, they
+still suffer from high latency. The root cause is that image
+enhancement models are much heavier than other computer
+vision models. For instance, the complexity of the SR model
+is as high as 1000× heavier than image classification, and
+object detection models in terms of MultAdds [12], as SR
+outputs high-resolution (HR) images whereas others output
+labels or Bounding boxes (Bbox). In other words, naively
+enhancing each frame is not practical in real-time video
+analytics applications.
+Fig. 3: Accuracy and latency using different schemes.
+As shown in Fig. 3, our preliminary study confirms the
+challenge in the tradeoff between accuracy and latency in
+video analytics. Due to resource restrictions, to use existing
+techniques in real-time and provide high accuracy, servers
+need to adaptively shift multiple pipelines, including inference
+after SR using HR frames, inference with low-resolution
+frames (LR), and reuse the last inference results. However,
+conventional algorithms (e.g., k-nearest neighbor (KNN) used
+in [6]) are largely suboptimal as they ignore the temporal
+relationship among frames and the possibility of transferring
+high-quality frames to the whole video. Therefore, we aim to
+design an efficient decoder to schedule the multiple pipelines
+for video analytics adaptively.
+III. SYSTEM DESIGN
+In this section, we present the design goals and our solution
+details of AccDecoder.
+Design goals. We take a pragmatic stance to focus on the
+server-side decoder because most of the installed surveil-
+lance or traffic cameras only have cheap CPUs without pro-
+grammable ability [6]; besides, rich information that may
+improve VAPs’ performance in the decoder has not been
+excavated. In this context, we propose AccDecoder, a portable
+tool/decoder which can be plugged into any VAPs for video
+streaming analytics to achieve high accuracy, limited latency
+(e.g., 30 ms), and low-resource goals simultaneously. As
+illustrated in Fig. 4, AccDecoder achieves these goals via the
+following three mechanisms: 1) Pipeline ‚ leverages SR model
+enhancing a small set of LR anchor frames to HR ones to
+achieve high accuracy. 2) Pipeline ƒ and Pipeline „ extract the
+codec information (e.g., frames reference relationship, MVs,
+and residuals) from the decoder, then utilize them to transfer
+the gains of enhanced anchor frames and reuse DNN inference
+
+results (e.g.. Bbox in object detection) onto the entire video
+respectively. Transfer and reuse amortize the computational
+overhead of SR and inference across the entire video and thus
+achieve low latency. 3) The scheduler classifies all frames into
+three subsets, and each executes one of three pipelines. It can
+greatly reduce latency and computational cost by exploiting
+the content features of the key frames (e.g., the intra-coded
+frame) and the change of codec information (e.g., residuals of
+continuous frames).
+content
+feature
+DRL
+reuse
+SR
+key frame
+residuals
+results
+AccDecoder
+HR
+inference
+LR
+HR
+bits stream
+motion
+vectors
+diff
+extractor
+decode
+decode
+scheduler
+transfer
+Fig. 4: Architecture of AccDecoder.
+Path towards the goal. We seek answers to the following
+pivotal questions, which lead to our key design choices. Q1
+— How to effectively transfer the gains of SR to up-scale non-
+anchor frames? Q2 — How to reuse the results of inference to
+the other frames? Q3 — How to assign appropriate decoding
+pipelines to frames in a fine spatial granularity to achieve a
+better accuracy-latency tradeoff than baselines?
+Q1 – How to transfer gains of SR to non-anchor frames?
+Approach: Pipeline ‚ + ƒ. To make the best of reuse,
+AccDecoder enhances anchor frames with the SR model and
+caches the output (see ‚ in Fig. 5); then it transfers the
+enhancement benefit to non-anchor frames with the reference
+information and the cached outputs (see ƒ in Fig. 5). This
+approach follows the same findings in [2] and [30], where most
+of the latency of SR occurs at the last couple of layers. Namely,
+caching and reusing the final output (i.e., high-resolution
+images) is most effective in achieving low latency.
+bits stream
+cache
+anchor frames
+motion
+vector
+scaling
+motion
+compensation
+residual
+interpolation
+SR transfer
+non-anchor
+frame
+SR
+reference
+SR caching
+Fig. 5: Process of SR gain transfer inspired by [30] and [27].
+Fig. 5 illustrates the process of transferring SR gains to a
+non-anchored frame for the inter-coded type. Modern video
+codec encodes/decodes frames on the basis of non-overlapped
+inter- and intra-coded blocks (§II-A). AccDecoder uses the
+reference index, MVs, and the residual in the codec infor-
+mation to decode a target block. The process is the same as
+normal decoding except for the additional SR, scaling, and in-
+terpolation modules (blue boxes in Fig. 5). First, AccDecoder
+selects the reference blocks among cached anchor frames
+following the inference index. Next, AccDecoder up-scales the
+MV with the same amplification factor as SR (e.g., from 270p
+to 1080 is 4). Following the MV, AccDecoder transfers the
+SR gain from the reference block in the cached frame to the
+target one. At last, AccDecoder up-scales the residual by light-
+weight interpolation (e.g., bilinear or bicubic), accumulates it
+to the transferred block to output the HR block, and pastes on
+the non-anchor frame. To the intra-coded blocks without the
+cached reference anchor frame, AccDecoder directly decodes
+and up-scales then by interpolation. Fortunately, with our
+carefully designed scheduler, most intra-coded blocks are
+assigned to the SR pipeline; the impact of the minority of
+interpolated intra-coded blocks can be negligible.
+Q2 — How to reuse inference results for non-inference frames?
+Approach: Pipeline „. AccDecoder infers inference frames
+using the inference model and caches the results; then, it uses
+the MVs and cached results to infer non-inference frames (see
+„ in Fig. 4). MV indicates the offset between the target and
+reference blocks (§II-A). Here we use the object detection
+task as an example, which aims to identify objects (i.e., their
+locations and classes) on each frame in videos. Fig. 6 reveals
+that the MVs between the last inference frame and the current
+frame can perfect match the movement of objects’ Bboxes
+(i.e., the results of object detection).
+Fig. 6: Relation between MVs and Bboxes.
+The Reuse module in Pipeline „ gets the result of the last
+inference frame (dotted line in Fig. 4), calculates the mean of
+all MVs that reside in each Bbox, and uses it to shift each Bbox
+to the current position. MV, as the block-level offset, is hard to
+express any semantic meaning (e.g., object moving) [34]. Our
+preliminary study implies that the accuracy of reuse degrades
+significantly after the MV, which spans multiple reference
+frames (e.g., over 7-10 frames in [7], [35], [36]).
+Optimization. AccDecoder uses two techniques to improve
+the accuracy of the reuse of inference results. First, it filters the
+noisy MVs from static backgrounds and outliers. Empirically,
+AccDecoder filters the MV whose value is equal to zero or
+greater than the mean plus 0.8 times the standard deviation in
+the Bbox to which it belongs. Second, to cope with the change
+in Bbox size due to the object’s movement, AccDecoder
+
+Motionvector
+Bbox of last inference frame
+口
+Bbox of current frameCON3a:8CON3a:CONexpands the MV calculation region to each direction by one
+macroblock (16 pixels). Note that the reuse module is not
+necessary to tackle but only remit this erosion because the
+scheduler module in (Q3) effectively controls it by judiciously
+distributing inference frames.
+Progress beyond the state of the art. Some prior work (e.g.,
+[37]–[39]) leverages lightweight MV-based methods to reuse
+analytics results and speed up inference. However, rather than
+calculating MV between continuous frames in the playback
+order like them, reuse in AccDecoder works in compressed-
+video space. That is, the reference blocks used to calculate
+the target block’s MV can be distributed throughout the video
+(the target block can even refer to future frames under the
+playback sequence, which is called backward reference)1, but
+the inference results should output in the playback order. To
+tackle this mismatch, we maintain a graph to map the coding
+order to the playback order and accumulate the MVs along the
+edges. Via statistical experiments on large-scale datasets, we
+find that the number of forwarding and backward references
+is less than 4 and 3 frames, respectively, so it is not time-
+consuming to search and calculate MVs in the graph.
+Q3 — How to guarantee accuracy-latency balance?
+Approach: Scheduler. The key to the accuracy-latency trade-
+off is how to optimally assign decoding pipelines (i.e., SR,
+inference, and reuse) to frames in fine spatial granularity.
+As analyzed in Fig. 3, different pipelines for frame decoding
+and analytics lead to different levels of accuracy and latency.
+For each frame in an SR class, selected anchor frames are
+enhanced by the SR model; after this, the scheduler feeds the
+up-scaling frame into the inference DNN for inference (e.g.,
+object detection). The frames in the inference class enjoy the
+benefits from the SR frames following the references in Fig. 5,
+and then are fed into the inference DNN model for inference.
+Their accuracy still increases due to the benefits transferred
+from the SR frames. Note that the transfer is quite fast (the
+time cost is the same as normal frame decoding) as it only
+includes additional bicubic interpolation on residual per frame
+compared to normal frame decoding. For those frames in the
+reuse class, e.g., object detection, we get the Bbox of each
+object in the last (playback order) detected frame, calculate
+the mean of all MVs that reside in the Bbox, and use it to
+shift the previous position to the current position.
+Model for pipeline selection. We formulate the adaptive
+pipeline selection problem to maximize the accuracy under the
+latency constraint. Given a video containing the set of frames
+F, one of the three pipelines is selected for each frame, which
+can be expressed as follows.
+max
+x
+�
+f∈F
+Acc(xf)
+s.t.
+�
+f∈F
+Latency(xf) ≤ τ,
+(1)
+1Modern video codecs aim at reducing video size; they only consider how
+to reduce the volume without caring whether the encoding obeys the playback
+order; thus coding order is very different from the playback order.
+where x = {x1, ..., xF } is the selection set and xf ∈ {1, 2, 3}
+is for pipeline selection, Acc is the accuracy of a frame,
+Latency is the latency of a frame given the selected pipeline,
+and τ is latency tolerant of frames F.
+(a) Correlations
+Frame
+34%
+(b) Time cost
+Fig. 7: Frame vs. residual in correlations between the dif-
+ference values and the changes of Bboxes, and time cost in
+feature extraction.
+Finding the optimal pipeline selection is tricky due to the
+large searching space 3|F |. Inspired by Reducto [6] which
+adaptively filters frame via setting a threshold on frame
+differencing, we introduce two thresholds tr1 and tr2 on frame
+differencing to cluster frames into tree pipelines. When the
+frame difference is greater than tr1, the frame will enter
+the pipeline ‚, and similarly, tr2 is the threshold for the
+pipeline ƒ. If the difference of a frame is greater than both
+of them, it will enter the pipeline‚. The constraint of real-
+time video analytics (e.g., speed of analytics ≥30fps) restricts
+us from extracting the light-weighted features to categorize
+frames. Different from [6], we find out the Laplacian (i.e.,
+edge features) on the residual and the frames have a high
+correlation with the inference accuracy (see Fig. 7(a)). At the
+same time, executing the Laplacian operator on the residual
+can save 34% time than that on frame (see Fig. 7(b)). One
+intuitive reason is that information on residuals is sparse and
+de-redundant. It preserves differences among frames but is not
+too dense to process, thus providing a good opportunity to
+categorize frames efficiently.
+best threshold
+<latexit sha1_base64="fVM29horhdM2tsOP41vyKZWto=">AB63icbVBNSwMxEJ3Ur1q/qh69BIvgqeyKqMeiF
+48V7Ae0S8m2TY0yS5JVihL/4IXD4p49Q9589+YbvegrQ8GHu/NMDMvTAQ31vO+UWltfWNzq7xd2dnd2z+oHh61TZxqylo0FrHuhsQwRVrW4F6yaERkK1gknd3O/8S04bF6tNOEBZKMFI84JTaX9MAfVGte3cuBV4lfkBoUaA6qX/1hTFPJlK
+WCGNPzvcQGdGWU8FmlX5qWELohIxYz1FJDNBlt86w2dOGeIo1q6Uxbn6eyIj0pipDF2nJHZslr25+J/XS210E2RcJali4WRanANsbzx/GQa0atmDpCqObuVkzHRBNqXTwVF4K/PIqaV/U/av65cNlrXFbxFGEziFc/DhGhpwD01oAYUxPM
+rvCGJXtA7+li0lAxcwx/gD5/ANuOjiE=</latexit>tr1
+<latexit sha1_base64="X7iO0S9KhHRkdM5ypW+Kp675Nrs=">AB63icbVBNS8NAEJ3Ur1q/qh69LBbBU0lKUY9FL
+x4r2A9oQ9lsN+3S3U3Y3Qgl9C948aCIV/+QN/+NmzQHbX0w8Hhvhpl5QcyZNq7ZQ2Nre2d8q7lb39g8Oj6vFJV0eJIrRDIh6pfoA15UzSjmG036sKBYBp71gdpf5vSeqNIvko5nH1Bd4IlnICDa5pEaNUbXm1t0caJ14BalBgfao+jUcRyQRVB
+rCsdYDz42Nn2JlGOF0URkmsaYzPCEDiyVWFDtp/mtC3RhlTEKI2VLGpSrvydSLSei8B2CmymetXLxP+8QWLCGz9lMk4MlWS5KEw4MhHKHkdjpigxfG4JorZWxGZYoWJsfFUbAje6svrpNuoe1f15kOz1rot4ijDGZzDJXhwDS24hzZ0gMAUnuE
+V3hzhvDjvzseyteQUM6fwB87nD90SjiI=</latexit>tr2
+(a) Video of crossroad
+best threshold
+<latexit sha1_base64="fVM29horhdM2tsOP41vyKZWto=">AB63icbVBNSwMxEJ3Ur1q/qh69BIvgqeyKqMeiF
+48V7Ae0S8m2TY0yS5JVihL/4IXD4p49Q9589+YbvegrQ8GHu/NMDMvTAQ31vO+UWltfWNzq7xd2dnd2z+oHh61TZxqylo0FrHuhsQwRVrW4F6yaERkK1gknd3O/8S04bF6tNOEBZKMFI84JTaX9MAfVGte3cuBV4lfkBoUaA6qX/1hTFPJlK
+WCGNPzvcQGdGWU8FmlX5qWELohIxYz1FJDNBlt86w2dOGeIo1q6Uxbn6eyIj0pipDF2nJHZslr25+J/XS210E2RcJali4WRanANsbzx/GQa0atmDpCqObuVkzHRBNqXTwVF4K/PIqaV/U/av65cNlrXFbxFGEziFc/DhGhpwD01oAYUxPM
+rvCGJXtA7+li0lAxcwx/gD5/ANuOjiE=</latexit>tr1
+<latexit sha1_base64="X7iO0S9KhHRkdM5ypW+Kp675Nrs=">AB63icbVBNS8NAEJ3Ur1q/qh69LBbBU0lKUY9FLx4r2A9oQ9lsN+3S3U3Y3Qgl9C948aCIV/+QN/+NmzQHbX0w8Hhvhpl5QcyZNq7ZQ2Nre2d8q7lb39g8Oj6vFJV0eJI
+rRDIh6pfoA15UzSjmG036sKBYBp71gdpf5vSeqNIvko5nH1Bd4IlnICDa5pEaNUbXm1t0caJ14BalBgfao+jUcRyQRVBrCsdYDz42Nn2JlGOF0URkmsaYzPCEDiyVWFDtp/mtC3RhlTEKI2VLGpSrvydSLSei8B2CmymetXLxP+8QWLCGz9lMk4MlWS5KEw4MhHKHkdjpigxfG4JorZWxGZYoWJsfFUbAje6svrpNuoe1f15kOz1rot4ijDGZzDJXhwDS24hzZ0gMAUnuEV3hzhvDjvzseyteQUM6fwB87nD90SjiI=</latexit>tr2
+(b) Video of highway
+Fig. 8: Best thresholds for pipeline selection vary across
+videos.
+Solution. Categorizing frames into three classes for pipelines
+
+is not trivial. Across various videos, their best threshold
+combination differs (as shown in Fig. 8). Furthermore, the
+optimal thresholds for frame feature differences (e.g., pixel
+and residual differences) among chunks in one video vary
+greatly. Fig. 9 plots the best thresholds on the videos in [35],
+which implies we should dynamically adjust the threshold for
+each chunk. Therefore, the scheduler needs to offer adaptive
+threshold settings.
+            
+<latexit sha1_base6
+4="fVM29horhdM2tsOP41vyKZWto=">AB
+63icbVBNSwMxEJ3Ur1q/qh69BIvgqeyKqMeiF
+48V7Ae0S8m2TY0yS5JVihL/4IXD4p49Q9589
++YbvegrQ8GHu/NMDMvTAQ31vO+UWltfWNzq7x
+d2dnd2z+oHh61TZxqylo0FrHuhsQwRVrW4F6
+yaERkK1gknd3O/8S04bF6tNOEBZKMFI84JT
+aX9MAfVGte3cuBV4lfkBoUaA6qX/1hTFPJlKW
+CGNPzvcQGdGWU8FmlX5qWELohIxYz1FJDNB
+lt86w2dOGeIo1q6Uxbn6eyIj0pipDF2nJHZsl
+r25+J/XS210E2RcJali4WRanANsbzx/GQa0
+atmDpCqObuVkzHRBNqXTwVF4K/PIqaV/U/av
+65cNlrXFbxFGEziFc/DhGhpwD01oAYUxPMr
+vCGJXtA7+li0lAxcwx/gD5/ANuOjiE=</lat
+exit>tr1
+            
+<latexit sha1_base64="X7iO0S9KhHRkdM5y
+pW+Kp675Nrs=">AB63icbVBNS8NAEJ3Ur1q/qh69LBbBU0lKUY9FLx4r2A9oQ9lsN+3S3U3Y
+3Qgl9C948aCIV/+QN/+NmzQHbX0w8Hhvhpl5QcyZNq7ZQ2Nre2d8q7lb39g8Oj6vFJV0eJIr
+RDIh6pfoA15UzSjmG036sKBYBp71gdpf5vSeqNIvko5nH1Bd4IlnICDa5pEaNUbXm1t0caJ14
+BalBgfao+jUcRyQRVBrCsdYDz42Nn2JlGOF0URkmsaYzPCEDiyVWFDtp/mtC3RhlTEKI2VLGp
+SrvydSLSei8B2CmymetXLxP+8QWLCGz9lMk4MlWS5KEw4MhHKHkdjpigxfG4JorZWxGZYoWJs
+fFUbAje6svrpNuoe1f15kOz1rot4ijDGZzDJXhwDS24hzZ0gMAUnuEV3hzhvDjvzseyteQUM6f
+wB87nD90SjiI=</latexit>tr2
+Chunk Index
+Inference Threshold
+SR Threshold
+Fig. 9: Best thresholds vary across chunks (even adjacent).
+To adaptively set the thresholds, we formulate this problem
+as a Markov decision process (MDP) where the scheduler
+makes the threshold setting decision in AccDecoder. The MDP
+is a discrete-time stochastic process, which can be defined by
+a quad-tuple < S, A, R, P >. In this tuple, S is the set of
+states, A is the set of actions, R is the set of rewards, and P
+is the probability of transition from state S to state S′ based
+on action A. While processing frames, the scheduler’s goal
+is to cluster them into three pipelines (i.e., the action A) to
+maximize its expected long-run reward E[Ri]. We define how
+the MDP is parameterized as follows.
+• State: The state consists of two components: the content
+feature of the key frame and the differencing features
+including inter-frame differences and difference between the
+key frame and the last inference frame. First, the features
+of the key frame (i.e., the first frame of the current chunk)
+are extracted through the 1x1x1000 fully connected FC-
+1000 layer of VGG16 [40]. Since the dimension of this
+feature is too large, we use principal component analysis
+(PCA) to reduce it to 128 dimensions. Next, we compute the
+inter-frame differences between every two frames of each
+chunk, which is the difference of edge features (i.e., apply
+the Laplacian operator to the residual of each frame) as
+discussed in Section III. Considering that there is continuity
+between chunks, it is also necessary to add information
+about inter-chunk, that is, the difference of edge features
+between the key frame and the last inference frame in the
+previous chunk.
+• Action: The action is to set two thresholds tr1 and tr2 for
+each chunk. The first threshold tr1 is applied to these frames
+to select anchor frames for SR and transfer their quality to
+the others for scale-up. The second one tr2 is to select
+inference frames that need to be analyzed by inference
+DNN. Then, the rest of the frames reuses the inference
+results by exploring frame reference. It is challenge to
+make accurate decisions for a large space of actions [41].
+Therefore, we discretize the action space to reduce the
+search space, i.e., tr1 ∈ {0.05, 0.10, 0.15, ..., 0.75} and
+tr2 ∈ {0.5, 1.0, ..., 2.5}.
+• Reward: Given that AccDecoder aims to maximize the
+inference accuracy within a tolerable latency. Therefore,
+the reward is designed to include two aspects, namely, the
+average accuracy of the chunk and the latency required
+to obtain the inference results for the chunk. Our goal is
+to achieve real-time inference, so the chunk needs to be
+analyzed before the arrival of the next chunk (e.g., within 1s
+for each chunk); otherwise, there is a penalty for exceeding
+the specified time. The reward for each chunk t is defined
+as follows.
+rt = α1
+|Ft|
+�
+f∈Ft
+Accf(trt,1, trt,2) − α2Pt(trt,1, trt,2), (2)
+where α1 and α2 are the weight factors to balance the pref-
+erence for latency and accuracy. The value of α in reward
+can be adjusted based on different service preferences and
+requirements. Pt is a penalty function of chunk t for latency
+exceeding the tolerance τ.
+Pt(trt,1, trt,2) =
+�
+1
+if Latency(trt,1, trt,2) > τ,
+0
+others.
+(3)
+The process of DRL in frame selection is shown below. At
+each chunk t, the agent observes the current state st and gives
+an action at according to its policy. Then, the environment
+returns reward rt as feedback, and moves to the next state
+st+1 according to the transition probability P(st+1|st, at).
+The goal to find an optimal policy can thus be formulated
+as the mathematical problem of maximizing the expectation
+of cumulative discounted return Rt = �T
+k=t γk−trk, where
+γ ∈ [0, 1] is a discount factor for future rewards to dampen
+the effect of future rewards on the action; rk is the reward of
+each step, and T is the number of chunks in the video.
+Computational complexity. The searching space of the op-
+timal pipeline selection for a chunk is O(3k), where k is
+the number of frames in the chunk. The searching space of
+AccDecoder’s scheduler is O(|a|), where |a| is the number of
+possible actions. As we discretize the action space, therefore,
+the complexity of AccDecoder is much less than that of
+optimal pipeline selection.
+IV. IMPLEMENTATION
+We implement AccDecoder as an intelligent decoder in
+both simulation and prototype. We first introduce the system
+settings of the experiment and the setup of the dataset and the
+baselines. Next, we introduce the training setup of AccDecoder
+on neural networks of DRL, SR, and inference.
+A. System Settings, Dataset, and Baselines
+System settings. The server component runs on an Ubuntu
+18.04 instance with Intel(R) Xeon(R) Gold 6226R CPU at
+2.90GHz and 1 NVIDIA GeForce RTX 3070 GPU. AccDe-
+coder is built on H.264 codec [42], JM 19.0 version open
+source code [43], with 2470 LoC changes. In practice, there
+are several video codecs besides H.264, but they have a high
+
+degree of similarity. For example, they share the same abstracts
+(i.e., reference index, MV, and residual), which are essential
+information to transfer neural super-resolution outputs to non-
+anchor frames. Their difference is in low-level compression
+algorithms (e.g., the number of reference frames and the
+size of blocks). Thus, while we only use H.264 to validate
+AccDecoder’s design, we believe the design is generic enough
+to accommodate different codecs.
+Dataset. Our video dataset mainly contains public data streams
+from real-time surveillance cameras deployed worldwide. We
+collected video clips of different scenes and times from differ-
+ent camera data sources. Thus, video datasets with different
+properties (e.g., time, illumination, vehicle and pedestrian
+density, road type, and direction) are obtained. All of our
+videos are available by searching on YouTube [35], [44], [45]
+and Yoda [7], [36], [46]. The videos are in 30fps, of which
+each chunk includes 30 frames (i.e., k = 30). In particular,
+VisDrone dataset [47] is used to train SR model. We use
+CityScapes [48] as dataset and results of ERFNet [49] to
+calculate inference loss for training.
+Baselines. We compare AccDecoder’s performance with the
+following four baselines: (1) Glimpse [24] filters frames by
+comparing pixel-level frame differences against a static thresh-
+old. (2) AWStream [10] adapts encoding parameters (i.e.,
+quantization parameter (QP), resolution, and frame rate) of the
+underlying codec to cope with different available bandwidth;
+(3) DDS [5] applies different quality encodings to different
+regions via region proposal network (RPN) [3], which can
+offer trade-off accuracy and latency. (4) Reducto [6] filters
+unnecessary frames in its encoder via a dynamic setting
+threshold given by the server to save bandwidth in uploading.
+B. DNN Implementation
+DRL settings. In the experiments, we set α1 = α2 = 0.5 and
+τ = 1s for each chunk according to our practical experience
+and requirements of services. We use an Adam optimizer
+with a learning rate of 0.0001. The discount factor for reward
+gamma is 0.99. We use a two-layer MLP with 128 units to
+implement the policy networks in DRL. The neural networks
+use ReLU as activation functions. The capacity of the replay
+buffer is 105, and we take a minibatch of 256 to update the
+network parameters.
+SR model. For object detection, we train the detection-driven
+SR model based on EDSR [50] following the analytics aware
+loss function (i.e., a weighted addition of visual quality loss
+and object detection inference loss) in [15]. We use VisDrone
+dataset [47] as the training set to train our model; use testing
+set from VisDrone, video set from DDS [5] and Reducto [6] to
+evaluate its performance. The visual quality loss comes from
+the pair of original and down sampling frames; the object
+detection inference loss comes from the results of YOLOv4 [1]
+detecting on reconstructed frames (from the down sampling
+frames) and the labels. The initial weights of EDSR and
+YOLOv4 are provided by authoritative implementations [1],
+[51]. The weights of EDSR are updated during our training,
+but the one of YOLOv4 keeps static.
+Inference DNN settings. We mainly evaluate AccDecoder’s
+performance on object detection. Here, we list the different
+DNNs used by AccDecoder for object detection. We choose
+two object detection models with different architectures in-
+cluding Faster R-CNN [3], YoLov5 [52]. We pre-trained both
+models using the COCO dataset [53].
+V. EVALUATION
+To demonstrate AccDecoder delivers significant quality im-
+provement, we compare AccDecoder with baselines in terms
+of inference accuracy and latency.
+A. Overall performance of AccDecoder
+Video quality improvement. We illustrate the performance
+of SR via Fig. 10, which shows the visual object detection
+results. The results vary in the original 1080p images with
+ground truth labels, inference results of low resolution (in
+270p), and inference results of up-scaled images by SR from
+270p. From the results, we can see SR delivers more detailed
+information to the DNN inference model, thus bounding more
+small objects and improving accuracy in object detection.
+(a) Ground truth (1080p)
+(b) Low resolution (270p)
+(c) Super resolution
+Fig. 10: SR can improve inference accuracy by enhancing
+resolution of frames in videos.
+Accuracy and latency. We demonstrate that AccDecoder
+can effectively improve accuracy-latency trade-off via adaptive
+pipeline assignment. Fig. 11 shows the per-chunk of pipeline
+assignment, accuracy (i.e., f1-score as a measure of accuracy),
+and speed of analytics, respectively. AccDecoder clusters
+frames into three types: 1) anchor frames (around 6%) are
+
+selected for pipeline ‚ with SR; 2) inference frames (11%)
+are analyzed by inference DNNs in pipeline ‚ and ƒ, in which
+5% frames are for pipeline ƒ; 3) non-inference and non-anchor
+frames (around 89%) are selected for pipeline „. Furthermore,
+AccDecoder and Reducto can achieve a higher frame rate than
+the basic requirement (i.e., 30fps), whereas other baselines
+offer a lower rate. AccDecoder can also achieve higher and
+more stable accuracy than the baselines. It is worth noting
+that from the 35th chunk, the density and velocity of vehicles
+increase significantly (i.e., 3x and 2.7x, respectively) so that
+the inferred rate is adjusted to a higher level, which ultimately
+maintains a good accuracy and frame rate.
+Pipeline
+Pipeline
+Pipeline
+> 85%
+density  3x
+velocity 2.7x
+base fps
+Chunk Index
+Fraction
+Chunk index
+0.00
+0.08
+0.16
+0.24
+0.80
+1.00
+AccDec.
+DDS
+Reducto
+Glimpse
+Awstream
+Fig. 11: Pipeline assignment ratio, analytics speed, and infer-
+ence accuracy of chunks.
+B. Component-wise Analysis
+Performance breakdown. We break down the accuracy and
+the latency to show the impact of each pipeline illustrated in
+Fig. 12. Firstly, Fig. 12(a) breakdowns the accuracy in transfer
+of anchor frames, reuse of the inference frames, and SR. The
+impact of reuse and SR on accuracy is obvious, while the
+impact of transfer is relatively small. The main reason is that
+the transfer has less improvement on small objects due to
+blur caused by interpolation, which will be one of our future
+works. Secondly, Fig. 12(b) shows the latency breakdown
+in processing each chunk, where we use videos in 270p,
+360p, and 540p, respectively. AccDecoder needs more time
+when processing and analyzing high-resolution videos, i.e.,
+the overall latency in ms. Specifically, SR (∼40%), inference
+(∼30%), and reuse (∼20%) take up most of the latency, while
+DRL-based scheduling and feature extraction only occupy
+around 5%, which can be omitted. SR is time-consuming,
+although only 6% of frames are assigned to pipeline ‚.
+Besides, inferring pipeline ‚ and ƒ for around 11% of frames
+also takes a latency that cannot be ignored. Although the time
+cost of reuse per frame is small, the time cost of reuse requires
+(a) Accuracy breakdown
+  1%
+36%
+29%
+42%
+  6%
+22%
+  1%
+27%
+49%
+  5%
+18%
+  1%
+40%
+  5%
+18%
+Resolution
+  1%
+36%
+29%
+42%
+  6%
+22%
+  1%
+27%
+49%
+  5%
+18%
+  1%
+40%
+  5%
+18%
+DRL
+Infer
+SR
+Feature
+Reuse
+Resolution
+Latency (ms)
+270p
+360p
+540p
+800
+600
+400
+200
+0
+(b) Latency breakdown
+Fig. 12: Performance breakdown on accuracy and latency.
+20% latency in total due to more than 85% frames belonging
+to pipeline „.
+AccDecoder schedulers. We evaluate the scheduler’s per-
+formance in AccDecoder, including DRL-based schemes and
+KNN, as illustrated in Fig. 13. We choose three well-known
+DRL schemes for training: Asynchronous Advantage Actor-
+Critic (A3C) [54], Soft Actor-Critic (SAC) [55], and Proximal
+Policy Optimization (PPO) [56]. Through effective explo-
+ration, we find A3C can receive a satisfactory and stable
+cumulative reward, which was about 11.42% higher than the
+cumulative reward received by KNN and PPO. From the final
+cumulative reward value in the figure, the cumulative rewards
+of A3C and SAC are higher. Considering the advantages of
+A3C, we choose A3C for the training of the scheduler.
+0
+500
+1000
+1500
+2000
+2500
+3000
+Episodes
+30
+32
+34
+36
+38
+40
+Reward
+A3C
+PPO
+SAC
+KNN
+Fig. 13: Comparison of different schemes for the scheduler
+in AccDecoder. DRL is better than KNN, and A3C achieves
+better learning performance than the others.
+
+1.00
+0.80.
+raction
+0.24
+0.16
+F
+0.08C. AccDecoder vs. Existing VAPs
+AccDecoder vs. baselines. We show the advantage of AccDe-
+coder in accuracy and speed of analytics compared with the
+baselines. Fig. 14 compares the performance distribution of
+AccDecoder with the baseline over different DNNs (YOLOv5
+and Faster R-CNN with Resnet50) and various types of videos
+(i.e., highways and crossroads). It can be seen that AccDecoder
+is better than the baseline in terms of speed and accuracy of
+analytics. In terms of speed, AccDecoder’s analytics speed is
+around 35fps, which meets the penalty threshold we set for
+DRL training. In terms of accuracy, AccDecoder can keep
+relatively higher accuracy compared with the baselines.
+0.2
+0.4
+0.6
+0.8
+F1-score
+0
+15
+30
+45
+FPS
+AccDec.
+DDS
+Reducto
+Glimpse
+AWStream
+Better
+(a) Faster R-CNN (highways)
+0.2
+0.4
+0.6
+0.8
+F1-score
+0
+15
+30
+45
+FPS
+AccDec.
+DDS
+Reducto
+Glimpse
+AWStream
+Better
+(b) Yolov5 (highways)
+0.2
+0.4
+0.6
+0.8
+F1-score
+0
+15
+30
+45
+FPS
+AccDec.
+DDS
+Reducto
+Glimpse
+AWStream
+Better
+(c) Faster R-CNN (crossroad)
+0.2
+0.4
+0.6
+0.8
+F1-score
+0
+15
+30
+45
+FPS
+AccDec.
+DDS
+Reducto
+Glimpse
+AWStream
+Better
+(d) Yolov5 (crossroad)
+Fig. 14: AccDecoder vs. baselines in terms of the speed of
+analytics and inference accuracy on various video datasets (in
+parentheses) and different DNN models (i.e., Faster R-CNN
+and Yolov5). AccDecoder achieves 6-38% higher inference
+accuracy than the baselines and 20-80% lower latency than
+the baselines except for Reducto.
+VI. RELATED WORKS
+Video analytics pipeline. Many computer vision tasks are
+considered in VAPs, such as traffic control [57], surveillance
+and security [11]. We consider the following task as a running
+example — object detection. Object detection aims to identify
+objects of interest (i.e., their locations and classes) in each
+frame in the video. Selecting this task has two major reasons:
+first, it plays a core role in the computer vision community
+because a wide range of high-level tasks (e.g., autonomous
+driving) is built on it; second, we seek to keep consistent
+with prior video analytics work [5], [58]–[60] to allow a
+straightforward performance comparison.
+Deep
+reinforcement
+learning. DRL is well suited to
+tackle problems requiring longer-term planning using high-
+dimensional observations, which is the case of dynamic
+pipeline selection. There is a variety of DRL-based algorithms.
+Value-based algorithms, e.g., Deep Q-Networks (DQN) [61],
+use a deep neural network to learn the action-value function.
+However, they do not support continuous action space like the
+one in our problem. Policy-based algorithms, e.g., Policy Gra-
+dient (PG) [62], explicitly build a representation of a policy.
+However, evaluating a policy without action-value estimation
+is typically inefficient and causes high variance. Actor-critic
+algorithms learn the value function (critic) in addition to the
+policy (actor) since knowing the value function can assist
+policy updates, for example, by reducing variance in policy
+gradients. Many existing approaches are based on actor-critic,
+for example, PPO [56], A3C [54], and SAC [55]. A3C, an
+asynchronous algorithm, can enable multiple worker agents to
+train in parallel, allowing faster training.
+VII. CONCLUSION AND DISCUSSION
+In this paper, we propose AccDecoder to eliminate the
+dependence of existing VAPs on video quality. AccDecoder
+is a new universal video stream decoder that uses a super-
+resolution deep neural network to enhance video quality for
+video analytics. To accelerate analytics, AccDecoder applies
+DRL for adaptive frame selection for quality enhancement
+or/and DNN-based inference. It is a new way to address the
+key challenge of accuracy-latency tradeoff in distributed VAPs.
+We show that AccDecoder can substantially improve state-of-
+the-art VAPs by speeding up analytics (3-7x) and achieving
+accuracy improvements (6-21%).
+In future work, we plan to explore DRL for macroblock
+selection to offer finer-grained scheduling and joint adaptation
+encoding and decoding to further improve the accuracy and
+speed of analytics.
+ACKNOWLEDGMENT
+This work has been partly funded by EU H2020 COSAFE
+(Grant 824019) and Horizon CODECO projects (Grant
+101092696), the Alexander von Humboldt Foundation, and
+the National Natural Science Foundation of China under Grant
+61872178, 62272223, and Grant 61832005.
+REFERENCES
+[1] A. Bochkovskiy, C.-Y. Wang, and H.-Y. M. Liao, “Yolov4: Optimal
+speed and accuracy of object detection,” in arXiv:2004.10934, 2020.
+[2] N. Ahn, B. Kang, and K.-A. Sohn, “Fast, accurate, and lightweight
+super-resolution with cascading residual network,” in Proc. of ECCV,
+2018, pp. 252–268.
+[3] S. Ren, K. He, R. Girshick, and J. Sun, “Faster R-CNN: Towards
+real-time object detection with region proposal networks,” Advances in
+Neural Information Processing Systems, vol. 28, 2015.
+[4] H. Wang, X. Jiang, H. Ren, Y. Hu, and S. Bai, “Swiftnet: Real-time
+video object segmentation,” in Proc. of CVPR, 2021, pp. 1296–1305.
+[5] K. Du, A. Pervaiz, X. Yuan, A. Chowdhery, Q. Zhang, H. Hoffmann, and
+J. Jiang, “Server-driven video streaming for deep learning inference,” in
+Proc. of ACM SIGCOMM, 2020, pp. 557–570.
+[6] Y. Li, A. Padmanabhan, P. Zhao, Y. Wang, G. H. Xu, and R. Netravali,
+“Reducto: On-camera filtering for resource-efficient real-time video
+analytics,” in Proc. of ACM SIGCOMM, 2020, pp. 359–376.
+[7] Yoda,
+“Crossroad
+video,”
+https://yoda.cs.uchicago.edu/videos/
+cross-road.mp4.
+[8] New York City Department of Transportation, “Real time traffic infor-
+mation,” https://webcams.nyctmc.org/, Mar. 2020.
+
+[9] P. Wei, H. Shi, J. Yang, J. Qian, Y. Ji, and X. Jiang, “City-scale vehicle
+tracking and traffic flow estimation using low frame-rate traffic cameras,”
+in Proc. of UbiComp/ISWC, 2019, pp. 602–610.
+[10] B. Zhang, X. Jin, S. Ratnasamy, J. Wawrzynek, and E. A. Lee,
+“Awstream: Adaptive wide-area streaming analytics.” in Proc. of ACM
+SIGCOMM, 2018, pp. 236–252.
+[11] J. Yi, S. Choi, and Y. Lee, “EagleEye: Wearable camera-based person
+identification in crowded urban spaces,” in Proc. of MobiCom, 2020.
+[12] J. Yi, S. Kim, J. Kim, and S. Choi, “Supremo: Cloud-assisted low-
+latency super-resolution in mobile devices,” IEEE Transactions on
+Mobile Computing, pp. 1847–1860, 2020.
+[13] J. Huang, V. Rathod, C. Sun, M. Zhu, A. Korattikara, A. Fathi, I. Fischer,
+Z. Wojna, Y. Song, S. Guadarrama et al., “Speed/accuracy trade-offs
+for modern convolutional object detectors,” in Proc. of CVPR, 2017, pp.
+7310–7311.
+[14] Y. Chen, Y. Tai, X. Liu, C. Shen, and J. Yang, “Fsrnet: End-to-end
+learning face super-resolution with facial priors,” in Proc. of CVPR,
+2018.
+[15] Y. Wang, W. Wang, D. Liu, X. Jin, J. Jiang, and K. Chen, “Enabling
+edge-cloud video analytics for robotics applications,” in Proc. of IEEE
+INFOCOM, 2022, pp. 1–10.
+[16] Z. Zou, Z. Shi, Y. Guo, and J. Ye, “Object detection in 20 years: A
+survey,” arXiv:1905.05055, 2019.
+[17] A. Ghodrati, B. E. Bejnordi, and A. Habibian, “Frameexit: Conditional
+early exiting for efficient video recognition,” in Proc. of CVPR, 2021,
+pp. 15 608–15 618.
+[18] A. Habibian, D. Abati, T. S. Cohen, and B. E. Bejnordi, “Skip-
+convolutions for efficient video processing,” in Proc. of CVPR, 2021,
+pp. 2695–2704.
+[19] N. C. Luong, D. T. Hoang, S. Gong, D. Niyato, P. Wang, Y.-C.
+Liang, and D. I. Kim, “Applications of deep reinforcement learning
+in communications and networking: A survey,” IEEE Communications
+Surveys & Tutorials, vol. 21, no. 4, pp. 3133–3174, 2019.
+[20] K. Arulkumaran, M. P. Deisenroth, M. Brundage, and A. A. Bharath, “A
+brief survey of deep reinforcement learning,” IEEE Signal Processing
+Magazine, vol. 34, no. 6, 2017.
+[21] T. Yuan, H.-M. Chung, J. Yuan, and X. Fu, “DACOM: Learning delay-
+aware communication for multi-agent reinforcement learning,” in Proc.
+of AAAI, 2023.
+[22] T. Yuan, C. E. Rothenberg, K. Obraczka, C. Barakat, and T. Turletti,
+“Harnessing UAVs for fair 5G bandwidth allocation in vehicular com-
+munication via deep reinforcement learning,” IEEE Transactions on
+Network and Service Management, vol. 18, no. 4, pp. 4063–4074, 2021.
+[23] T. Yuan, W. da Rocha Neto, C. E. Rothenberg, K. Obraczka, C. Barakat,
+and T. Turletti, “Dynamic controller assignment in software defined
+internet of vehicles through multi-agent deep reinforcement learning,”
+IEEE Transactions on Network and Service Management, vol. 18, no. 1,
+pp. 585–596, 2020.
+[24] T. Y.-H. Chen, L. Ravindranath, S. Deng, P. Bahl, and H. Balakrishnan,
+“Glimpse: Continuous, real-time object recognition on mobile devices,”
+in Proc. of SenSys, 2015, pp. 155–168.
+[25] Boulder AI, “Dnncam ai camera,” https://groupgets.com/campaigns/
+429-dnncam-ai-camera.
+[26] NVIDIA,
+“Jetson
+tx2,”
+https://www.nvidia.com/de-de/
+autonomous-machines/embedded-systems/jetson-tx2.
+[27] T. Wiegand, G. J. Sullivan, G. Bjontegaard, and A. Luthra, “Overview of
+the H. 264/AVC video coding standard,” IEEE Transactions on Circuits
+and Systems for Video Technology, vol. 13, no. 7, pp. 560–576, 2003.
+[28] M. Dasari, A. Bhattacharya, S. Vargas, P. Sahu, A. Balasubramanian,
+and S. R. Das, “Streaming 360-degree videos using super-resolution,”
+in Proc. of IEEE INFOCOM, 2020, pp. 1977–1986.
+[29] J. Kim, Y. Jung, H. Yeo, J. Ye, and D. Han, “Neural-enhanced live
+streaming: Improving live video ingest via online learning,” in Proc. of
+ACM SIGCOMM, 2020, pp. 107–125.
+[30] H. Yeo, C. J. Chong, Y. Jung, J. Ye, and D. Han, “Nemo: enabling neural-
+enhanced video streaming on commodity mobile devices,” in Proc. of
+MobiCom, 2020, pp. 1–14.
+[31] H. Yeo, Y. Jung, J. Kim, J. Shin, and D. Han, “Neural adaptive content-
+aware internet video delivery,” in Proc. of OSDI 18, 2018, pp. 645–661.
+[32] Y. Wang, W. Wang, J. Zhang, J. Jiang, and K. Chen, “Bridging the
+edge-cloud barrier for real-time advanced vision analytics,” in Proc. of
+HotCloud, 2019.
+[33] T. Zhang, A. Chowdhery, P. Bahl, K. Jamieson, and S. Banerjee, “The
+design and implementation of a wireless video surveillance system,” in
+Proc. of MobiCom, 2015, pp. 426–438.
+[34] H. Yeo, S. Do, and D. Han, “How will deep learning change internet
+video delivery?” in Proc. of ACM HotNets, 2017, pp. 57–64.
+[35] Youtube, “Gebhardt insurance traffic cam round trip bike shop,” https:
+//www.youtube.com/watch?v= XBMMTQVj68.
+[36] Yoda, “Highway video,” https://yoda.cs.uchicago.edu/videos/highway.
+mp4.
+[37] J. Zhang, D. Zhang, X. Xu, F. Jia, Y. Liu, X. Liu, J. Ren, and Y. Zhang,
+“MobiPose: Real-time multi-person pose estimation on mobile devices,”
+in Proc. of SenSys, 2020, pp. 136–149.
+[38] R. Xu, C.-l. Zhang, P. Wang, J. Lee, S. Mitra, S. Chaterji, Y. Li,
+and S. Bagchi, “ApproxDet: content and contention-aware approximate
+object detection for mobiles,” in Proc. of SenSys, 2020, pp. 449–462.
+[39] L. Liu, H. Li, and M. Gruteser, “Edge assisted real-time object detection
+for mobile augmented reality,” in Proc. of MobiCom, 2019, pp. 1–16.
+[40] K. Simonyan and A. Zisserman, “Very deep convolutional networks for
+large-scale image recognition,” in Proc. of ICLR, 2015, pp. 602–610.
+[41] S. Yan, X. Wang, X. Zheng, Y. Xia, D. Liu, and W. Deng, “ACC:
+Automatic ECN tuning for high-speed datacenter networks,” in Proc. of
+ACM SIGCOMM, 2021, pp. 384–397.
+[42] Google,
+“libvpx
+official
+github
+repository,”
+https://github.com/
+webmproject/libvpx/.
+[43] Open Source, “Jm 19.0,” https://iphome.hhi.de/suehring/.
+[44] Youtube, “Jackson hole wyoming usa town square live cam,” https://
+www.youtube.com/watch?v=1EiC9bvVGnk.
+[45] Youtube, “City of auburn toomer’s corner webcam,” https://www.
+youtube.com/watch?v=hMYIc5ZPJL4.
+[46] Yoda, “Motorway video,” https://yoda.cs.uchicago.edu/videos/motorway.
+mp4.
+[47] H. Fan, D. Du, L. Wen, P. Zhu, Q. Hu, H. Ling, M. Shah, J. Pan,
+A. Schumann, B. Dong et al., “Visdrone-mot2020: The vision meets
+drone multiple object tracking challenge results,” in Proc. of ECCV,
+2020, pp. 713–727.
+[48] M. Cordts, M. Omran, S. Ramos, T. Rehfeld, M. Enzweiler, R. Be-
+nenson, U. Franke, S. Roth, and B. Schiele, “The cityscapes dataset
+for semantic urban scene understanding,” in Proc. of CVPR, 2016, pp.
+3213–3223.
+[49] E. Romera, J. M. Alvarez, L. M. Bergasa, and R. Arroyo, “Erfnet: Effi-
+cient residual factorized convnet for real-time semantic segmentation,”
+IEEE Transactions on Intelligent Transportation Systems, vol. 19, no. 1,
+pp. 263–272, 2017.
+[50] B. Lim, S. Son, H. Kim, S. Nah, and K. Mu Lee, “Enhanced deep
+residual networks for single image super-resolution,” in Proc. of CVPR,
+2017, pp. 136–144.
+[51] B. Lim, S. Son, H. Kim, S. Nah, and K. M. Lee, “Enhanced deep residual
+networks for single image super-resolution,” in Proc. of CVPR, 2017.
+[52] J. Redmon and A. Farhadi, “Yolo9000: better, faster, stronger.” in Proc.
+of CVPR, 2017.
+[53] C. dataset, “highway video,” https://cocodataset.org/.
+[54] V. Mnih, A. P. Badia, M. Mirza, A. Graves, T. Lillicrap, T. Harley,
+D. Silver, and K. Kavukcuoglu, “Asynchronous methods for deep
+reinforcement learning,” in Proc. of ICML, 2016.
+[55] T. Haarnoja, A. Zhou, P. Abbeel, and S. Levine, “Soft actor-critic: Off-
+policy maximum entropy deep reinforcement learning with a stochastic
+actor,” in Proc. of ICML, 2018, pp. 1861–1870.
+[56] J. Schulman, F. Wolski, P. Dhariwal, A. Radford, and O. Klimov,
+“Proximal policy optimization algorithms,” arXiv:1707.06347, 2017.
+[57] G. Ananthanarayanan, P. Bahl, P. Bod´ık, K. Chintalapudi, M. Philipose,
+L. Ravindranath, and S. Sinha, “Real-time video analytics: The killer
+app for edge computing,” IEEE Computer, vol. 50, no. 10, pp. 58–67,
+2017.
+[58] J. Jiang, G. Ananthanarayanan, P. Bodik, S. Sen, and I. Stoica,
+“Chameleon: scalable adaptation of video analytics,” in Proc. of ACM
+SIGCOMM, 2018, pp. 253–266.
+[59] S. Jain, X. Zhang, Y. Zhou, G. Ananthanarayanan, J. Jiang, Y. Shu,
+V. Bahl, and J. Gonzalez, “Spatula: Efficient cross-camera video analyt-
+ics on large camera networks,” in Proc. ACM SEC, 2020, pp. 110–124.
+[60] Y. Yuan, W. Wang, Y. Wang, S. S. Adhatarao, B. Ren, K. Zheng, and
+X. Fu, “VSiM: Improving QoE fairness for video streaming in mobile
+environments,” in Proc. of IEEE INFOCOM, 2022, pp. 1309–1318.
+
+[61] V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G.
+Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski
+et al., “Human-level control through deep reinforcement learning,”
+Nature, vol. 518, no. 7540, pp. 529–533, 2015.
+[62] R. S. Sutton, D. A. McAllester, S. P. Singh, Y. Mansour et al., “Policy
+gradient methods for reinforcement learning with function approxima-
+tion.” in Proc. of NIPS, vol. 99, 1999, pp. 1057–1063.
+