# First-order Convergence Theory for Weakly-Convex-Weakly-Concave Min-max Problems

@article{Liu2021FirstorderCT, title={First-order Convergence Theory for Weakly-Convex-Weakly-Concave Min-max Problems}, author={Mingrui Liu and Hassan Rafique and Qihang Lin and Tianbao Yang}, journal={J. Mach. Learn. Res.}, year={2021}, volume={22}, pages={169:1-169:34} }

In this paper, we consider first-order convergence theory and algorithms for solving a class of non-convex non-concave min-max saddle-point problems, whose objective function is weakly convex in the variables of minimization and weakly concave in the variables of maximization. It has many important applications in machine learning including training Generative Adversarial Nets (GANs). We propose an algorithmic framework motivated by the inexact proximal point method, where the weakly monotone…

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