Near-Optimal Algorithms for Making the Gradient Small in Stochastic Minimax Optimization

• URL: http://arxiv.org/abs/2208.05925v1
• Date: Thu, 11 Aug 2022 16:55:26 GMT
• Title: Near-Optimal Algorithms for Making the Gradient Small in Stochastic Minimax Optimization
• Authors: Lesi Chen, Luo Luo
• Abstract summary: We study the problem of finding a near-stationary point for smooth minimax optimization. We show that a novel algorithm called Recursive IteratioNRAIN achieves both convex-concave and strongly-concave cases.
• Score: 14.719077076351377
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the problem of finding a near-stationary point for smooth minimax optimization. The recent proposed extra anchored gradient (EAG) methods achieve the optimal convergence rate for the convex-concave minimax problem in deterministic setting. However, the direct extension of EAG to stochastic optimization is not efficient. In this paper, we design a novel stochastic algorithm called Recursive Anchored IteratioN (RAIN). We show that the RAIN achieves near-optimal stochastic first-order oracle complexity for stochastic minimax optimization in both convex-concave and strongly-convex-strongly-concave cases.

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