Zeroth-order single-loop algorithms for nonconvex-linear minimax problems

Nonconvex minimax problems have attracted significant interest in machine learning and many other fields in recent years. In this paper, we propose a new zeroth-order alternating randomized gradient projection algorithm to solve smooth nonconvex-linear problems and its iteration complexity to find a...

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Vydáno v:Journal of global optimization Ročník 87; číslo 2-4; s. 551 - 580
Hlavní autoři: Shen, Jingjing, Wang, Ziqi, Xu, Zi
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.11.2023
Springer
Témata:
Algorithms
Computer Science
Game theory
Machine learning
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Complexity analysis
90C30
90C47
Alternating randomized gradient projection algorithm
Machine learning
90C26
Nonconvex-linear minimax problem
Zeroth-order algorithm
Alternating randomized proximal gradient algorithm
ISSN:0925-5001, 1573-2916
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Shrnutí:Nonconvex minimax problems have attracted significant interest in machine learning and many other fields in recent years. In this paper, we propose a new zeroth-order alternating randomized gradient projection algorithm to solve smooth nonconvex-linear problems and its iteration complexity to find an ε -first-order Nash equilibrium is O ε - 3 and the number of function value estimation per iteration is bounded by O d x ε - 2 . Furthermore, we propose a zeroth-order alternating randomized proximal gradient algorithm for block-wise nonsmooth nonconvex-linear minimax problems and its corresponding iteration complexity is O K 3 2 ε - 3 and the number of function value estimation is bounded by O d x ε - 2 per iteration. The numerical results indicate the efficiency of the proposed algorithms.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-022-01169-5