Min-max problems have broad applications in machine learning including learning with non-decomposable loss and learning with robustness to data's distribution. Although convex-concave min-max problems have been broadly studied with efficient algorithms and solid theories available, it still remains a challenge to design provably efficient algorithms for non-convex min-max problems. Motivated by the applications in machine learning, this paper studies a family of non-convex min-max problems, whose objective function is weakly convex in the variables of minimization and is concave in the variable of maximization. We propose a proximally guided stochastic subgradient method and a proximally guided stochastic variance-reduced method for this class of problems under different assumptions. We establish their time complexities for finding a nearly stationary point of the outer minimization problem corresponding to the min-max problem.
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