Zeroth-Order Alternating Gradient Descent Ascent Algorithms for a Class of Nonconvex-Nonconcave Minimax Problems

• URL: http://arxiv.org/abs/2211.13668v2
• Date: Sat, 27 May 2023 02:50:40 GMT
• Title: Zeroth-Order Alternating Gradient Descent Ascent Algorithms for a Class of Nonconvex-Nonconcave Minimax Problems
• Authors: Zi Xu, Zi-Qi Wang, Jun-Lin Wang, Yu-Hong Dai
• Abstract summary: We propose a zeroth-order alternating gradient descent ascent (ZO-AGDA) algorithm for solving the NC-PL minimax problem. To the best of our knowledge, they are the first two zeroth-order algorithms with the complexity gurantee for solving NC-PL minimax problems.
• Score: 9.792800635198935
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we consider a class of nonconvex-nonconcave minimax problems, i.e., NC-PL minimax problems, whose objective functions satisfy the Polyak-\L ojasiewicz (PL) condition with respect to the inner variable. We propose a zeroth-order alternating gradient descent ascent (ZO-AGDA) algorithm and a zeroth-order variance reduced alternating gradient descent ascent (ZO-VRAGDA) algorithm for solving NC-PL minimax problem under the deterministic and the stochastic setting, respectively. The total number of function value queries to obtain an $\epsilon$-stationary point of ZO-AGDA and ZO-VRAGDA algorithm for solving NC-PL minimax problem is upper bounded by $\mathcal{O}(\varepsilon^{-2})$ and $\mathcal{O}(\varepsilon^{-3})$, respectively. To the best of our knowledge, they are the first two zeroth-order algorithms with the iteration complexity gurantee for solving NC-PL minimax problems.

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