Work

Derivative-Free Alternating Projection Algorithms for General Nonconvex-Concave Minimax Problems

Year: 2024

Type: article

Abstract: . In this paper, we study zeroth-order algorithms for nonconvex-concave minimax problems, which have attracted much attention in machine learning, signal processing, and many other fields in recent years. We propose a zeroth-order alternating randomized gradient projection (ZO-AGP) algorithm for smooth nonconvex-concave minimax problems; its iteration complexity to obtain an [Formula: see text]-stationary point is bounded by [Formula: see text], and the number of function value estimates is bounded by [Formula: see text] per iteration. Moreover, we propose a zeroth-order block alternating randomized proximal gradient algorithm (ZO-BAPG) for solving blockwise nonsmooth nonconvex-concave minimax optimization problems; its iteration complexity to obtain an [Formula: see text]-stationary point is bounded by [Formula: see text], and the number of function value estimates per iteration is bounded by [Formula: see text]. To the best of our knowledge, this is the first time zeroth-order algorithms with iteration complexity guarantee are developed for solving both general smooth and blockwise nonsmooth nonconvex-concave minimax problems. Numerical results on the data poisoning attack problem and the distributed nonconvex sparse principal component analysis problem validate the efficiency of the proposed algorithms.

Source: SIAM Journal on Optimization

DOI: 10.1137/23m1568168

Authors: Zi Xu, Ziqi Wang, Jingjing Shen, Yuhong Dai

Institutions: Shanghai University, Chinese Academy of Sciences, Academy of Mathematics and Systems Science

Language: English

Topic: Stochastic Gradient Optimization Techniques

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Chinese Academy of Sciences

Awards: G3553588891, G3907981520, G622688436, 非凸极小极大优化问题的理论、算法及应用研究