Zeroth-Order Alternating Randomized Gradient Projection Algorithms for General Nonconvex-Concave Minimax Problems
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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 ε-stationary point is bounded by 𝒪(ε^-4), and the number of function value estimation is bounded by 𝒪(d_xε^-4+d_yε^-6) 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 ε-stationary point is bounded by 𝒪(ε^-4) and the number of function value estimation per iteration is bounded by 𝒪(K d_xε^-4+d_yε^-6). 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 validate the efficiency of the proposed algorithms.
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