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 ϵ-stationary point of ZO-AGDA and ZO-VRAGDA algorithm for solving NC-PL minimax problem is upper bounded by O(ε−2) and O(ε−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.
@article{arxiv.2211.13668,
title = {Zeroth-Order Alternating Gradient Descent Ascent Algorithms for a Class of Nonconvex-Nonconcave Minimax Problems},
author = {Zi Xu and Zi-Qi Wang and Jun-Lin Wang and Yu-Hong Dai},
journal= {arXiv preprint arXiv:2211.13668},
year = {2023}
}