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 ...
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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 alternatingrandomizedgradientprojection (ZO-AGP) algorithm for smooth nonconvex-concave minimax problems;its iteration complexity to obtain an \varepsilon -stationary point is bounded by O( \varepsilon - 4 ), and the number of function value estimates is bounded by O( d x + d y ) per iteration. Moreover, we propose a zeroth -order block alternatingrandomized proximal gradientalgorithm (ZO-BAPG) for solving blockwise nonsmooth nonconvexconcave minimax optimization problems;its iteration complexity to obtain an \varepsilon -stationary point is bounded by O( \varepsilon - 4 ), and the number of function value estimates per iteration is bounded by O( Kd x + d y ). 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.
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