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DERIVATIVE-FREE ALTERNATING PROJECTION ALGORITHMS FOR GENERAL NONCONVEX-CONCAVE MINIMAX PROBLEMS.
- Source :
- SIAM Journal on Optimization; 2024, Vol. 34 Issue 2, p1879-1908, 30p
- Publication Year :
- 2024
-
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 varepsilon -stationary point is bounded by crO (\varepsilon 4), and the number of function value estimates is bounded by scrO (dx + dy) per iteration. Moreover, we propose a zeroth-order block alternating randomized proximal gradient algorithm (ZO-BAPG) for solving blockwise nonsmooth nonconvexconcave minimax optimization problems; its iteration complexity to obtain an varepsilon -stationary point is bounded by scrO (varepsilon 4), and the number of function value estimates per iteration is bounded by O (Kdx +dy). 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10526234
- Volume :
- 34
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- SIAM Journal on Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 178370491
- Full Text :
- https://doi.org/10.1137/23M1568168