MARS: Unleashing the Power of Variance Reduction for Training Large Models

Abstract

Training deep neural networks—and more recently, large models—demands efficient and scalable optimizers. Adaptive gradient algorithms like Adam, AdamW, and their variants have been central to this task. Despite the development of numerous variance reduction algorithms in the past decade aimed at accelerating stochastic optimization in both convex and nonconvex settings, variance reduction has not found widespread success in training deep neural networks or large language models. Consequently, it has remained a less favored approach in modern AI. In this paper, to unleash the power of variance reduction for efficient training of large models, we propose a unified optimization framework, MARS (Make vAriance Reduction Shine), which reconciles preconditioned gradient methods with variance reduction via a scaled stochastic recursive momentum technique. Within our framework, we introduce three instances of MARS that leverage preconditioned gradient updates based on AdamW, Lion, Shampoo, respectively. We also draw a connection between our algorithms and existing optimizers. Experimental results on training GPT-2 models indicate that MARS consistently outperforms AdamW by a large margin.

About MARS

MARS (Make vAriance Reduction Shine) is a unified optimization framework designed to address the inherent challenges of training large models. Traditional adaptive gradient methods like Adam and AdamW often suffer from high stochastic gradient variance, while variance reduction techniques have struggled to gain practical impact in deep learning. At its core, MARS comprises two major components: (1) a scaled stochastic recursive momentum, which provides a variance-reduced estimator of the full gradient for better gradient complexity; and (2) the preconditioned update, which approximates the second-order Newton's method for better per-iteration complexity. By combining preconditioned gradient methods with variance reduction, MARS achieves the best of both worlds, accelerating the search for critical points in optimization.

MARS consistently outperforms AdamW and the Muon optimizer across GPT-2 models. More details and code releases are at https://github.com/AGI-Arena/MARS.