An accelerated first-order regularized momentum descent ascent algorithm for stochastic nonconvex-concave minimax problems

Stochastic nonconvex minimax problems have attracted wide attention in machine learning, signal processing and many other fields in recent years. In this paper, we propose an accelerated first-order regularized momentum descent ascent algorithm (FORMDA) for solving stochastic nonconvex-concave minim...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 90; no. 2; pp. 557 - 582
Main Authors: Zhang, Huiling, Xu, Zi
Format: Journal Article
Language:English
Published: New York Springer Nature B.V 01.03.2025
Subjects:
Algorithms
Complexity
Machine learning
Methods
Minimax technique
Momentum
Optimization
Random variables
Signal processing
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Summary:Stochastic nonconvex minimax problems have attracted wide attention in machine learning, signal processing and many other fields in recent years. In this paper, we propose an accelerated first-order regularized momentum descent ascent algorithm (FORMDA) for solving stochastic nonconvex-concave minimax problems. The iteration complexity of the algorithm is proved to be O~(ε-6.5) to obtain an ε-stationary point, which achieves the best-known complexity bound for single-loop algorithms to solve the stochastic nonconvex-concave minimax problems under the stationarity of the objective function.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-024-00638-9