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This paper focuses on stochastic methods for solving smooth non-convexstrongly-concave min-max problems, which have received increasing attention dueto their potential applications in deep learning (e.g., deep AUC maximization,distributionally robust optimization). However, most of the existing algorithmsare slow in practice, and their analysis revolves around the convergence to anearly stationary point.We consider leveraging the Polyak-Lojasiewicz (PL)condition to design faster stochastic algorithms with stronger convergenceguarantee. Although PL condition has been utilized for designing manystochastic minimization algorithms, their applications for non-convex min-maxoptimization remain rare. In this paper, we propose and analyze a genericframework of proximal stage-based method with many well-known stochasticupdates embeddable. Fast convergence is established in terms of both the primalobjective gap and the duality gap. Compared with existing studies, (i) ouranalysis is based on a novel Lyapunov function consisting of the primalobjective gap and the duality gap of a regularized function, and (ii) theresults are more comprehensive with improved rates that have better dependenceon the condition number under different assumptions. We also conduct deep andnon-deep learning experiments to verify the effectiveness of our methods.

Fast Objective & Duality Gap Convergence for Non-Convex Strongly-Concave Min-Max Problems with PL Condition