Distributed Extra-gradient with Optimal Complexity and Communication Guarantees

TL;DR

This paper introduces a communication-efficient, quantized version of the extra-gradient algorithm for distributed monotone variational inequality problems, achieving optimal convergence rates and validated through real-world multi-GPU experiments.

Contribution

The paper proposes Q-GenX, an unbiased adaptive compression method for distributed VI problems, with adaptive step-size and optimal convergence guarantees.

Findings

Achieves ${ m O}(1/T)$ convergence under relative noise.

Achieves ${ m O}(1/ oot 2 T)$ convergence under absolute noise.

Validated through training GANs on multiple GPUs.

Abstract

We consider monotone variational inequality (VI) problems in multi-GPU settings where multiple processors/workers/clients have access to local stochastic dual vectors. This setting includes a broad range of important problems from distributed convex minimization to min-max and games. Extra-gradient, which is a de facto algorithm for monotone VI problems, has not been designed to be communication-efficient. To this end, we propose a quantized generalized extra-gradient (Q-GenX), which is an unbiased and adaptive compression method tailored to solve VIs. We provide an adaptive step-size rule, which adapts to the respective noise profiles at hand and achieve a fast rate of ${\mathcal O}(1/T)$ under relative noise, and an order-optimal ${\mathcal O}(1/\sqrt{T})$ under absolute noise and show distributed training accelerates convergence. Finally, we validate our theoretical results by providing real-world experiments and training generative adversarial networks on multiple GPUs.