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

In this paper, we study zeroth-order algorithms for nonconvex-concave minimax problems, which have attracted widely 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, and its iteration complexity to obtain an varepsilon-stationary point is bounded by O(varepsilon-4), and the number of function value estimation is bounded by O(dx+dy) per iteration. Moreover, we propose a zeroth-order block alternating randomized proximal gradient algorithm (ZO-BAPG) for solving block-wise nonsmooth nonconvex-concave minimax optimization problems, and the iteration complexity to obtain an varepsilon-stationary point is bounded by O(varepsilon-4) and the number of function value estimation per iteration is bounded by O(K dx+dy). To the best of our knowledge, this is the first time that zeroth-order algorithms with iteration complexity gurantee are developed for solving both general smooth and block-wise nonsmooth nonconvex-concave minimax problems. Numerical results on data poisoning attack problem and distributed nonconvex sparse principal component analysis problem validate the efficiency of the proposed algorithms.