Local exponential stability of mean-field Langevin descent-ascent and associated particle system

Excerpt

arXiv:2602.01564v3 Announce Type: replace Abstract: We study the mean-field Langevin descent-ascent (MFL-DA), a coupled optimization dynamics on the space of probability measures for entropically regularized two-player zero-sum games, together with its associated interacting particle system. For general nonconvex-nonconcave payoffs, Wang and Chizat (COLT 2024) asked whether the original single-timescale MFL-DA converges to the mixed Nash equilibrium and, if so, at what rate. We prove a local aff