Sampling from the Mean-Field Stationary Distribution
Abstract
We study the complexity of sampling from the stationary distribution of a mean-field SDE, or equivalently, the complexity of minimizing a functional over the space of probability measures which includes an interaction term. Our main insight is to decouple the two key aspects of this problem: (1) approximation of the mean-field SDE via a finite-particle system, via uniform-in-time propagation of chaos, and (2) sampling from the finite-particle stationary distribution, via standard log-concave samplers. Our approach is conceptually simpler and its flexibility allows for incorporating the state-of-the-art for both algorithms and theory. This leads to improved guarantees in numerous settings, including better guarantees for optimizing certain two-layer neural networks in the mean-field regime. A key technical contribution is to establish a new uniform-in- log-Sobolev inequality for the stationary distribution of the mean-field Langevin dynamics.
Cite
@article{arxiv.2402.07355,
title = {Sampling from the Mean-Field Stationary Distribution},
author = {Yunbum Kook and Matthew S. Zhang and Sinho Chewi and Murat A. Erdogdu and Mufan Bill Li},
journal= {arXiv preprint arXiv:2402.07355},
year = {2024}
}