Daily Papers

Mediation analysis learns the causal effect transmitted via mediator variables between treatments and outcomes and receives increasing attention in various scientific domains to elucidate causal relations. Most existing works focus on point-exposure studies where each subject only receives one treatment at a single time point. However, there are a number of applications (e.g., mobile health) where the treatments are sequentially assigned over time and the dynamic mediation effects are of primary interest. Proposing a reinforcement learning (RL) framework, we are the first to evaluate dynamic mediation effects in settings with infinite horizons. We decompose the average treatment effect into an immediate direct effect, an immediate mediation effect, a delayed direct effect, and a delayed mediation effect. Upon the identification of each effect component, we further develop robust and semi-parametrically efficient estimators under the RL framework to infer these causal effects. The superior performance of the proposed method is demonstrated through extensive numerical studies, theoretical results, and an analysis of a mobile health dataset.

Multi-modal AI systems will likely become a ubiquitous presence in our everyday lives. A promising approach to making these systems more interactive is to embody them as agents within physical and virtual environments. At present, systems leverage existing foundation models as the basic building blocks for the creation of embodied agents. Embedding agents within such environments facilitates the ability of models to process and interpret visual and contextual data, which is critical for the creation of more sophisticated and context-aware AI systems. For example, a system that can perceive user actions, human behavior, environmental objects, audio expressions, and the collective sentiment of a scene can be used to inform and direct agent responses within the given environment. To accelerate research on agent-based multimodal intelligence, we define "Agent AI" as a class of interactive systems that can perceive visual stimuli, language inputs, and other environmentally-grounded data, and can produce meaningful embodied action with infinite agent. In particular, we explore systems that aim to improve agents based on next-embodied action prediction by incorporating external knowledge, multi-sensory inputs, and human feedback. We argue that by developing agentic AI systems in grounded environments, one can also mitigate the hallucinations of large foundation models and their tendency to generate environmentally incorrect outputs. The emerging field of Agent AI subsumes the broader embodied and agentic aspects of multimodal interactions. Beyond agents acting and interacting in the physical world, we envision a future where people can easily create any virtual reality or simulated scene and interact with agents embodied within the virtual environment.

We present The Matrix, the first foundational realistic world simulator capable of generating continuous 720p high-fidelity real-scene video streams with real-time, responsive control in both first- and third-person perspectives, enabling immersive exploration of richly dynamic environments. Trained on limited supervised data from AAA games like Forza Horizon 5 and Cyberpunk 2077, complemented by large-scale unsupervised footage from real-world settings like Tokyo streets, The Matrix allows users to traverse diverse terrains -- deserts, grasslands, water bodies, and urban landscapes -- in continuous, uncut hour-long sequences. Operating at 16 FPS, the system supports real-time interactivity and demonstrates zero-shot generalization, translating virtual game environments to real-world contexts where collecting continuous movement data is often infeasible. For example, The Matrix can simulate a BMW X3 driving through an office setting--an environment present in neither gaming data nor real-world sources. This approach showcases the potential of AAA game data to advance robust world models, bridging the gap between simulations and real-world applications in scenarios with limited data.

We study infinite-horizon average-reward Markov decision processes (AMDPs) in the context of general function approximation. Specifically, we propose a novel algorithmic framework named Local-fitted Optimization with OPtimism (LOOP), which incorporates both model-based and value-based incarnations. In particular, LOOP features a novel construction of confidence sets and a low-switching policy updating scheme, which are tailored to the average-reward and function approximation setting. Moreover, for AMDPs, we propose a novel complexity measure -- average-reward generalized eluder coefficient (AGEC) -- which captures the challenge of exploration in AMDPs with general function approximation. Such a complexity measure encompasses almost all previously known tractable AMDP models, such as linear AMDPs and linear mixture AMDPs, and also includes newly identified cases such as kernel AMDPs and AMDPs with Bellman eluder dimensions. Using AGEC, we prove that LOOP achieves a sublinear mathcal{O}(poly(d, sp(V^*)) Tbeta ) regret, where d and beta correspond to AGEC and log-covering number of the hypothesis class respectively, sp(V^*) is the span of the optimal state bias function, T denotes the number of steps, and mathcal{O} (cdot) omits logarithmic factors. When specialized to concrete AMDP models, our regret bounds are comparable to those established by the existing algorithms designed specifically for these special cases. To the best of our knowledge, this paper presents the first comprehensive theoretical framework capable of handling nearly all AMDPs.

Understanding the loss landscape is an important problem in machine learning. One key feature of the loss function, common to many neural network architectures, is the presence of exponentially many low lying local minima. Physical systems with similar energy landscapes may provide useful insights. In this work, we point out that black holes naturally give rise to such landscapes, owing to the existence of black hole entropy. For definiteness, we consider 1/8 BPS black holes in N = 8 string theory. These provide an infinite family of potential landscapes arising in the microscopic descriptions of corresponding black holes. The counting of minima amounts to black hole microstate counting. Moreover, the exact numbers of the minima for these landscapes are a priori known from dualities in string theory. Some of the minima are connected by paths of low loss values, resembling mode connectivity. We estimate the number of runs needed to find all the solutions. Initial explorations suggest that Stochastic Gradient Descent can find a significant fraction of the minima.

The construction of a theory of quantum gravity is an outstanding problem that can benefit from better understanding the laws of nature that are expected to hold in regimes currently inaccessible to experiment. Such fundamental laws can be found by considering the classical counterparts of a quantum theory. For example, conservation laws in a quantum theory often stem from conservation laws of the corresponding classical theory. In order to construct such laws, this thesis is concerned with the interplay between symmetries and conservation laws of classical field theories and their application to asymptotically flat spacetimes. This work begins with an explanation of symmetries in field theories with a focus on variational symmetries and their associated conservation laws. Boundary conditions for general relativity are then formulated on three-dimensional asymptotically flat spacetimes at null infinity using the method of conformal completion. Conserved quantities related to asymptotic symmetry transformations are derived and their properties are studied. This is done in a manifestly coordinate independent manner. In a separate step a coordinate system is introduced, such that the results can be compared to existing literature. Next, asymptotically flat spacetimes which contain both future as well as past null infinity are considered. Asymptotic symmetries occurring at these disjoint regions of three-dimensional asymptotically flat spacetimes are linked and the corresponding conserved quantities are matched. Finally, it is shown how asymptotic symmetries lead to the notion of distinct Minkowski spaces that can be differentiated by conserved quantities.

We provide a mapping between past null and future null infinity in three-dimensional flat space, using symmetry considerations. From this we derive a mapping between the corresponding asymptotic symmetry groups. By studying the metric at asymptotic regions, we find that the mapping is energy preserving and yields an infinite number of conservation laws.

Formulating a quantum theory of gravity lies at the heart of fundamental theoretical physics. This collection of lecture notes encompasses a selection of topics that were covered in six mini-courses at the Nordita PhD school "Towards Quantum Gravity". The scope was to provide a coherent picture, from its foundation to forefront research, emphasizing connections between different areas. The lectures begin with perturbative quantum gravity and effective field theory. Subsequently, two ultraviolet-complete approaches are presented: asymptotically safe gravity and string theory. Finally, elements of quantum effects in black hole spacetimes are discussed.

We present metrics for measuring state similarity in Markov decision processes (MDPs) with infinitely many states, including MDPs with continuous state spaces. Such metrics provide a stable quantitative analogue of the notion of bisimulation for MDPs, and are suitable for use in MDP approximation. We show that the optimal value function associated with a discounted infinite horizon planning task varies continuously with respect to our metric distances.

Markov Decision Processes (MDPs) are a formal framework for modeling and solving sequential decision-making problems. In finite-time horizons such problems are relevant for instance for optimal stopping or specific supply chain problems, but also in the training of large language models. In contrast to infinite horizon MDPs optimal policies are not stationary, policies must be learned for every single epoch. In practice all parameters are often trained simultaneously, ignoring the inherent structure suggested by dynamic programming. This paper introduces a combination of dynamic programming and policy gradient called dynamic policy gradient, where the parameters are trained backwards in time. For the tabular softmax parametrisation we carry out the convergence analysis for simultaneous and dynamic policy gradient towards global optima, both in the exact and sampled gradient settings without regularisation. It turns out that the use of dynamic policy gradient training much better exploits the structure of finite-time problems which is reflected in improved convergence bounds.

We study the problem of estimating the distribution of the return of a policy using an offline dataset that is not generated from the policy, i.e., distributional offline policy evaluation (OPE). We propose an algorithm called Fitted Likelihood Estimation (FLE), which conducts a sequence of Maximum Likelihood Estimation (MLE) and has the flexibility of integrating any state-of-the-art probabilistic generative models as long as it can be trained via MLE. FLE can be used for both finite-horizon and infinite-horizon discounted settings where rewards can be multi-dimensional vectors. Our theoretical results show that for both finite-horizon and infinite-horizon discounted settings, FLE can learn distributions that are close to the ground truth under total variation distance and Wasserstein distance, respectively. Our theoretical results hold under the conditions that the offline data covers the test policy's traces and that the supervised learning MLE procedures succeed. Experimentally, we demonstrate the performance of FLE with two generative models, Gaussian mixture models and diffusion models. For the multi-dimensional reward setting, FLE with diffusion models is capable of estimating the complicated distribution of the return of a test policy.

We propose a new method for optimistic planning in infinite-horizon discounted Markov decision processes based on the idea of adding regularization to the updates of an otherwise standard approximate value iteration procedure. This technique allows us to avoid contraction and monotonicity arguments typically required by existing analyses of approximate dynamic programming methods, and in particular to use approximate transition functions estimated via least-squares procedures in MDPs with linear function approximation. We use our method to recover known guarantees in tabular MDPs and to provide a computationally efficient algorithm for learning near-optimal policies in discounted linear mixture MDPs from a single stream of experience, and show it achieves near-optimal statistical guarantees.

Mirror descent value iteration (MDVI), an abstraction of Kullback-Leibler (KL) and entropy-regularized reinforcement learning (RL), has served as the basis for recent high-performing practical RL algorithms. However, despite the use of function approximation in practice, the theoretical understanding of MDVI has been limited to tabular Markov decision processes (MDPs). We study MDVI with linear function approximation through its sample complexity required to identify an varepsilon-optimal policy with probability 1-delta under the settings of an infinite-horizon linear MDP, generative model, and G-optimal design. We demonstrate that least-squares regression weighted by the variance of an estimated optimal value function of the next state is crucial to achieving minimax optimality. Based on this observation, we present Variance-Weighted Least-Squares MDVI (VWLS-MDVI), the first theoretical algorithm that achieves nearly minimax optimal sample complexity for infinite-horizon linear MDPs. Furthermore, we propose a practical VWLS algorithm for value-based deep RL, Deep Variance Weighting (DVW). Our experiments demonstrate that DVW improves the performance of popular value-based deep RL algorithms on a set of MinAtar benchmarks.

Many existing reinforcement learning (RL) methods employ stochastic gradient iteration on the back end, whose stability hinges upon a hypothesis that the data-generating process mixes exponentially fast with a rate parameter that appears in the step-size selection. Unfortunately, this assumption is violated for large state spaces or settings with sparse rewards, and the mixing time is unknown, making the step size inoperable. In this work, we propose an RL methodology attuned to the mixing time by employing a multi-level Monte Carlo estimator for the critic, the actor, and the average reward embedded within an actor-critic (AC) algorithm. This method, which we call Multi-level Actor-Critic (MAC), is developed especially for infinite-horizon average-reward settings and neither relies on oracle knowledge of the mixing time in its parameter selection nor assumes its exponential decay; it, therefore, is readily applicable to applications with slower mixing times. Nonetheless, it achieves a convergence rate comparable to the state-of-the-art AC algorithms. We experimentally show that these alleviated restrictions on the technical conditions required for stability translate to superior performance in practice for RL problems with sparse rewards.

Off-policy evaluation (OPE) is a method for estimating the return of a target policy using some pre-collected observational data generated by a potentially different behavior policy. In some cases, there may be unmeasured variables that can confound the action-reward or action-next-state relationships, rendering many existing OPE approaches ineffective. This paper develops an instrumental variable (IV)-based method for consistent OPE in confounded Markov decision processes (MDPs). Similar to single-stage decision making, we show that IV enables us to correctly identify the target policy's value in infinite horizon settings as well. Furthermore, we propose an efficient and robust value estimator and illustrate its effectiveness through extensive simulations and analysis of real data from a world-leading short-video platform.

We introduce and describe tt GrayHawk, a publicly available Mathematica-based tool designed for the efficient computation of gray-body factors for spherically symmetric and asymptotically flat black holes. This program provides users with a rapid and reliable means to compute gray-body factors for massless fields with spin \(s = 0, 1/2, 1, 2\) in modes specified by the angular quantum number \(l\), given a black hole metric and the associated parameter values. tt GrayHawk is preloaded with seven different black hole metrics, offering immediate applicability to a variety of theoretical models. Additionally, its modular structure allows users to extend its functionality easily by incorporating alternative metrics or configurations. This versatility makes tt GrayHawk a powerful and adaptable resource for researchers studying black hole physics and Hawking radiation. The codes described in this work are publicly available at https://github.com/marcocalza89/GrayHawk.

To deepen our understanding of Quantum Gravity and its connections with black holes and cosmology, building a common language and exchanging ideas across different approaches is crucial. The Nordita Program "Quantum Gravity: from gravitational effective field theories to ultraviolet complete approaches" created a platform for extensive discussions, aimed at pinpointing both common grounds and sources of disagreements, with the hope of generating ideas and driving progress in the field. This contribution summarizes the twelve topical discussions held during the program and collects individual thoughts of speakers and panelists on the future of the field in light of these discussions.

We discuss relevant scalar deformations of a holographic theory with a compact boundary. An example of such a theory would be the global AdS_4 with its spatially compact boundary S^2. To introduce a relevant deformation, we choose to turn on a time-independent and spatially homogeneous non-normalizable scalar operator with m^2 = -2. The finite size of a compact boundary cuts down the RG flow at a finite length scale leading to an incomplete RG flow to IR. We discuss a version of {\it incomplete} C-theorem and an {\it incomplete} attractor like mechanism. We discuss the implication of our results for entanglement entropy and geometric quantities like scalar curvature, volume and mass scale of fundamental excitation of the how these quantities increase or decrease (often monotonically) with the strength of the deformation. Thermal physics of a holographic theory defined on a compact boundary is more interesting than its non-compact counterpart. It is well known that with a compact boundary, there is a possibility of a first order Hawking-Page transition dual to a de-confinement phase transition. From a gravity perspective, a relevant deformation dumps negative energy inside the bulk, increasing the effective cosmological constant (Lambda) of the AdS. Dumping more negative energy in the bulk would make the HP transition harder and the corresponding HP transition temperature would increase. However, we have found the size of the BH at the transition temperature decreases.

A major outstanding challenge in cosmology is the persistent discrepancy between the Hubble constant obtained from early and late universe measurements -- the Hubble tension. Examining cosmological evolution through the lens of information growth within a black hole we show the appearence of two fractal growing processes characterizing the early and late ages. These fractals induce space growth rates of 62.79pm5.59 km/s/Mpc and 70.07pm0.09 km/s/Mpc; close to the current values of the Hubble constants involved in the tension. These results strongly suggest that the Hubble tension is not given by unexpected large-scale structures or multiple, unrelated errors but by innate properties underlying the universe dynamics.

Non-trivial gravitational saddles have played a key role in the island proposal for the black hole information paradox. It is worth asking if non-trivial saddles exist in microscopic descriptions of black holes. We show this to be the case for 1/8 BPS black holes in N = 8 String Theory in a duality frame, where all charges are Ramond Ramond. The saddles are in the Coulomb branch, where they describe marginally stable bound states of the constituent branes, and correspond to vacua of the BFSS model. The non-perturbative suppression scale is determined by the binding energy.

JWST has detected many overmassive galactic systems at z > 4, where the mass of the black hole, M_bullet, is 10-100 times larger than expected from local relations, given the host's stellar mass, M_star. This Letter presents a model to describe these overmassive systems in the high-z Universe. We suggest that the black hole mass is the main driver of high-z star formation quenching. SMBHs globally impact their high-z galaxies because their hosts are physically small, and the black holes have duty cycles close to unity at z > 4. In this regime, we assume that black hole mass growth is regulated by the quasar's output, while stellar mass growth is quenched by it and uncorrelated to the global properties of the host halo. We find that the ratio M_bullet/M_star controls the average star formation efficiency: if M_bullet/M_star > 8times 10^{18} (n Lambda/f_{edd})[(Omega_b M_h)/(Omega_m M_star) - 1], then the galaxy is unable to form stars efficiently. Once this ratio exceeds the threshold, a runaway process brings the originally overmassive system towards the local M_bullet - M_star relation. Furthermore, the M_bullet - M_star relation evolves with redshift as propto (1+z)^{5/2}. At z sim 5, we find an overmassive factor of sim 55, in excellent agreement with current JWST data and the high-z relation inferred from those. Extending the black hole horizon farther in redshift and lower in mass will test this model and improve our understanding of the early co-evolution of black holes and galaxies.