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