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arXiv · 2208.05925

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

Lesi Chen·Luo Luo
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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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Lesi Chen, Luo Luo. 2022-08-11. Near-Optimal Algorithms for Making the Gradient Small in Stochastic Minimax Optimization. https://arxiv.org/abs/2208.05925

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