Nesterov Meets Optimism: Rate-Optimal Separable Minimax Optimization

• URL: http://arxiv.org/abs/2210.17550v2
• Date: Mon, 14 Aug 2023 18:18:05 GMT
• Title: Nesterov Meets Optimism: Rate-Optimal Separable Minimax Optimization
• Authors: Chris Junchi Li, Angela Yuan, Gauthier Gidel, Quanquan Gu, Michael I. Jordan
• Abstract summary: We propose a new first-order optimization algorithm -- AcceleratedGradient-OptimisticGradient (AG-OG) Ascent. We show that AG-OG achieves the optimal convergence rate (up to a constant) for a variety of settings. We extend our algorithm to extend the setting and achieve the optimal convergence rate in both bi-SC-SC and bi-C-SC settings.
• Score: 108.35402316802765
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a new first-order optimization algorithm -- AcceleratedGradient-OptimisticGradient (AG-OG) Descent Ascent -- for separable convex-concave minimax optimization. The main idea of our algorithm is to carefully leverage the structure of the minimax problem, performing Nesterov acceleration on the individual component and optimistic gradient on the coupling component. Equipped with proper restarting, we show that AG-OG achieves the optimal convergence rate (up to a constant) for a variety of settings, including bilinearly coupled strongly convex-strongly concave minimax optimization (bi-SC-SC), bilinearly coupled convex-strongly concave minimax optimization (bi-C-SC), and bilinear games. We also extend our algorithm to the stochastic setting and achieve the optimal convergence rate in both bi-SC-SC and bi-C-SC settings. AG-OG is the first single-call algorithm with optimal convergence rates in both deterministic and stochastic settings for bilinearly coupled minimax optimization problems.

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