Stochastic Recursive Gradient Descent Ascent for Stochastic Nonconvex-Strongly-Concave Minimax Problems
Luo Luo, Haishan Ye, Zhichao Huang, Tong Zhang
Abstract
We consider nonconvex-concave minimax optimization problems of the form minx maxy?Y f(x, y), where f is strongly-concave in y but possibly nonconvex in x and Y is a convex and compact set. We focus on the stochastic setting, where we can only access an unbiased stochastic gradient estimate of f at each iteration. This formulation includes many machine learning applications as special cases such as robust optimization and adversary training. We are interested in finding an O(e)-stationary point of the function F(·) = maxy?Y f(·, y). The most popular algorithm to solve this problem is stochastic gradient decent ascent, which requires O(?3e-4) stochastic gradient evaluations, where ? is the condition number. In this paper, we propose a novel method called Stochastic Recursive gradiEnt Descent Ascent (SREDA), which estimates gradients more efficiently using variance reduction. This method achieves the best known stochastic gradient complexity of O(?3e-3), and its dependency on e is optimal for this problem. © 2020 Neural information processing systems foundation. All rights reserved.