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arXiv · 2602.16517

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

Jean-Christophe Mourrat
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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.

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Jean-Christophe Mourrat. 2026-02-18. PL conditions do not guarantee convergence of gradient descent-ascent dynamics. https://arxiv.org/abs/2602.16517

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