Distributed Extra-gradient with Optimal Complexity and Communication Guarantees
Keywords: Unbiased Quantization, Variational Inequality, Extra-gradient, Adaptive Sep-size
TL;DR: We propose quantized generalized extra-gradient, which is an unbiased and adaptive compression method tailored to a generic unifying framework for solving variational inequality problems.
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 ${\cal O}(1/T)$ under relative noise, and an order-optimal ${\cal O}(1/\sqrt{T})$ 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.
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Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2308.09187/code)
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