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Single-Loop Stochastic Projected Damped Extragradient Methods for Stochastic Nonconvex--(Strongly) Concave Minimax Optimization

arXiv · AI, language, vision and robotics · article · Sep 18, 2026 · UTC

We develop single-loop stochastic projected damped extragradient methods for stochastic nonconvex--(strongly) concave minimax optimization, with complexity guarantees for both game stationarity (GS) and optimization stationarity (OS). Our approach combines a stochastic projected damped extragradient (SPDE) method with a recursive variance-reduced variant, VR-SPDE, both of which retain a single-loop structure. Under an unbiased stochastic gradient oracle with uniformly bounded variance, SPDE finds an $\varepsilon$-game-stationary point with stochastic first-order oracle (SFO) complexities of $O

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