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Uniform-in-Time Propagation of Chaos for Mean Field Langevin Dynamics

Chen, Fan; Ren, Zhenjie; Wang, Songbo (2022), Uniform-in-Time Propagation of Chaos for Mean Field Langevin Dynamics. https://basepub.dauphine.psl.eu/handle/123456789/23740

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Type
Document de travail / Working paper
Date
2022
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
31
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Author(s)
Chen, Fan
School of Mathematical Sciences [Shanghai]
Ren, Zhenjie
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Wang, Songbo
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Abstract (EN)
We study the uniform-in-time propagation of chaos for mean field Langevin dynamics with convex mean field potenital. Convergences in both Wasserstein-2 distance and relative entropy are established. We do not require the mean field potenital functional to bear either small mean field interaction or displacement convexity, which are common constraints in the literature. In particular, it allows us to study the efficiency of the noisy gradient descent algorithm for training two-layer neural networks.