Distributed Extra-gradient with Optimal Complexity and Communication Guarantees

• URL: http://arxiv.org/abs/2308.09187v1
• Date: Thu, 17 Aug 2023 21:15:04 GMT
• Title: Distributed Extra-gradient with Optimal Complexity and Communication Guarantees
• Authors: Ali Ramezani-Kebrya and Kimon Antonakopoulos and Igor Krawczuk and Justin Deschenaux and Volkan Cevher
• Abstract summary: We consider monotone variational inequality (VI) problems in multi-GPU settings where multiple processors/workers/clients have access to local dual vectors. Extra-gradient, which is a de facto algorithm for monotone VI problems, has not been designed to be communication-efficient. We propose a quantized generalized extra-gradient (Q-GenX), which is an unbiased and adaptive compression method tailored to solve VIs.
• Score: 60.571030754252824
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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