PreprintCC BY 4.0HAL
PL conditions do not guarantee convergence of gradient descent-ascent dynamics
Abstract
We give an example of a function satisfying a two-sided Polyak-Łojasiewicz 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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BibTeX
@misc{mourrat2026conditions,
title = {{PL conditions do not guarantee convergence of gradient descent-ascent dynamics}},
author = {Jean-Christophe Mourrat},
howpublished = {HAL},
year = {2026},
month = oct,
eprint = {2602.16517},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05777135v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - PL conditions do not guarantee convergence of gradient descent-ascent dynamics
AU - Jean-Christophe Mourrat
PY - 2026
DA - 2026/10/04
PB - HAL
UR - https://hal.science/hal-05777135v1
AB - We give an example of a function satisfying a two-sided Polyak-Łojasiewicz 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.
ER -