Weakly-convex–concave min–max optimization: provable algorithms and applications in machine learning

Min–max problems have broad applications in machine learning, including learning with non-decomposable loss and robustness to data distribution. Convex–concave min–max problem is an active topic of research efficient algorithms sound theoretical foundations developed. However, it remains a challenge design provably for non-convex or without smoothness. In this paper, we study family problems, whose objective function weakly convex the variables minimization concave maximization. We propose proximally guided stochastic subgradient method variance-reduced non-smooth smooth instances, respectively, problems. analyse time complexities proposed methods finding nearly stationary point outer corresponding problem.