arXiv：cs.LG· Geuntaek Seo, Minseop Shin, Pierre Monmarch\'e, Beomjun Choi·· 7 小时前AI 评分30
MFL-DA 的局部指数稳定性及其关联粒子系统
Local exponential stability of mean-field Langevin descent-ascent and associated particle system
AI 导读
针对熵正则化双人零和博弈的耦合优化动力学 MFL-DA，该研究证明了局部收敛性：当初值足够接近混合 Nash 均衡时，平均场动力学以可量化的速率指数收敛至该均衡。其有限 N 粒子系统在直至 N 的指数时间内继承该稳定性，收敛速率与 N 无关，仅存在有限粒子误差下限。
正文
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 affirmative answer in Wasserstein space: if the initial datum is sufficiently close to the mixed Nash equilibrium, then the mean-field dynamics converges to it exponentially fast at a quantitative rate. We further show that the finite-$N$ particle system inherits this stability up to times exponential in $N$, with an $N$-independent exponential rate modulo a finite-particle error floor. Combined with the recent counterexample of Mourrat and Pillaud-Vivien for MFL-DA, which shows that global convergence cannot hold in general, our theorem completes the positive local counterpart of the Wang-Chizat question: the mixed Nash equilibrium has a robust basin of attraction, stable under both the mean-field flow and its finite-particle approximation.
| Comments: | Revised and reorganized manuscript |
| Subjects: | Machine Learning (cs.LG); Analysis of PDEs (math.AP); Optimization and Control (math.OC); Probability (math.PR) |
| MSC classes: | 49Q22, 90C47, 35Q84, 35B40 |
| Cite as: | arXiv:2602.01564 [cs.LG] |
| (or arXiv:2602.01564v3 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2602.01564 arXiv-issued DOI via DataCite |
Submission history
From: Beomjun Choi [view email]
[v1]
Mon, 2 Feb 2026 02:58:17 UTC (54 KB)
[v2]
Thu, 2 Jul 2026 08:10:11 UTC (61 KB)
[v3]
Tue, 6 Oct 2026 14:33:29 UTC (84 KB)
来源：arXiv：cs.LG · arxiv.org