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

Huiling Zhang and Zi Xu ()
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Huiling Zhang: Shanghai University
Zi Xu: Shanghai University

Computational Optimization and Applications, 2025, vol. 90, issue 2, No 8, 557-582

Abstract: Abstract 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 $$\tilde{\mathcal {O}}(\varepsilon ^{-6.5})$$ O ~ ( ε - 6.5 ) to obtain an $$\varepsilon $$ 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.

Keywords: Stochastic nonconvex minimax problem; Accelerated momentum projection gradient algorithm; Iteration complexity; Machine learning (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10589-024-00638-9

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