Review for NeurIPS paper: A Single-Loop Smoothed Gradient Descent-Ascent Algorithm for Nonconvex-Concave Min-Max Problems

Neural Information Processing Systems 

The title used for the paper is misleading since the rate O(epsilon {-2}) can only be achieved for a special class of non-convex concave min-max problems. More specifically, this rate is attained when using the algorithm to minimize the pointwise maximum of finite collection of non-convex functions. For general non-convex concave the rate is O(epsilon {-4}). This is clarified in the body of the paper, but the title is clearly misleading. It is not clear in the paper when this assumption (or even its relaxed replacement in the appendix) holds in practice.