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Main Authors: Chen, Lesi, Luo, Luo
Format: Preprint
Published: 2022
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Online Access:https://arxiv.org/abs/2208.05925
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author Chen, Lesi
Luo, Luo
author_facet Chen, Lesi
Luo, Luo
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2208_05925
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Near-Optimal Algorithms for Making the Gradient Small in Stochastic Minimax Optimization
Chen, Lesi
Luo, Luo
Machine Learning
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.
title Near-Optimal Algorithms for Making the Gradient Small in Stochastic Minimax Optimization
topic Machine Learning
url https://arxiv.org/abs/2208.05925