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

Atsushi Nitanda; Matthew S. Zhang; Sinho Chewi

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

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arxiv 2409.10440 v1 pith:477KFXEA submitted 2024-09-16 math.PR

Sinho Chewi , Atsushi Nitanda , Matthew S. Zhang This is my paper · ORCID

classification math.PR

keywords dynamicsinequalitylangevinlog-sobolevmean-fieldconstantconvexdistribution

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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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