Uniform-in-$N$ log-Sobolev inequality for the mean-field Langevin dynamics with convex energy

Sinho Chewi; Atsushi Nitanda; Matthew S. Zhang

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arXiv · 2409.10440

Uniform-in-$N$ log-Sobolev inequality for the mean-field Langevin dynamics with convex energy

Sinho Chewi·Atsushi Nitanda·Matthew S. Zhang

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Abstract

We establish a log-Sobolev inequality for the stationary distribution of mean-field Langevin dynamics with a constant that is independent of the number of particles $N$. Our proof proceeds by establishing the existence of a Lipschitz transport map from the standard Gaussian measure via the reverse heat flow of Kim and Milman.

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Sinho Chewi, Atsushi Nitanda, Matthew S. Zhang. 2024-09-16. Uniform-in-$N$ log-Sobolev inequality for the mean-field Langevin dynamics with convex energy. https://arxiv.org/abs/2409.10440

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