A Single-Loop Stochastic Gradient Algorithm for Minimax Optimization with Nonlinear Coupled Constraints
Abstract
In this paper, we propose a single-loop stochastic gradient algorithm for solving stochastic nonconvex-concave minimax optimization with nonlinear convex coupled constraints (MCC). The proposed method, SPACO (Stochastic Penalty-based Algorithm for minimax optimization with COupled constraints), is built upon a penalty-based smooth approximation framework for MCC. This framework integrates a quadratic penalty scheme with regularization to yield a continuously differentiable approximation of the MCC problem. We provide theoretical convergence guarantees for this smoothing framework. Furthermore, we establish non-asymptotic complexity bounds and provide an asymptotic analysis characterizing the stationarity of accumulation points for the iterates generated by SPACO. Experimental results on synthetic examples and practical machine learning tasks demonstrate the effectiveness and efficiency of the proposed method.
Cite
@article{arxiv.2605.01246,
title = {A Single-Loop Stochastic Gradient Algorithm for Minimax Optimization with Nonlinear Coupled Constraints},
author = {Qichao Cao and Shangzhi Zeng and Jin Zhang and Yuxuan Zhou},
journal= {arXiv preprint arXiv:2605.01246},
year = {2026}
}