PL conditions do not guarantee convergence of gradient descent-ascent dynamics

Abstract

We give an example of a function satisfying a two-sided Polyak-Lojasiewicz condition but for which a gradient descent-ascent flow line fails to converge to the saddle point, circling around it instead. We can even impose the function to be strongly convex in one variable and to satisfy a PL condition in the other variable.

arXiv comment17 pages. V3: final version