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

• URL: http://arxiv.org/abs/2208.05925v4
• Date: Mon, 03 Feb 2025 17:42:21 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 the RAIN (SFO) achieves minimax optimization in both convexconcave-concave cases.
• Score: 17.467589890017123
• License:
• Abstract: We study the problem of finding a near-stationary point for smooth minimax optimization. The recently proposed extra anchored gradient (EAG) methods achieve the optimal convergence rate for the convex-concave minimax problem in the 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 (SFO) complexity for stochastic minimax optimization in both convex-concave and strongly-convex-strongly-concave cases. In addition, we extend the idea of RAIN to solve structured nonconvex-nonconcave minimax problem and it also achieves near-optimal SFO complexity.

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