Ergodicity of the underdamped mean-field Langevin dynamics

Kazeykina, Anna; Ren, Zhenjie; Tan, Xiaolu; Yang, Junjian

Kazeykina, Anna; Ren, Zhenjie; Tan, Xiaolu; Yang, Junjian (2020), Ergodicity of the underdamped mean-field Langevin dynamics. https://basepub.dauphine.fr/handle/123456789/21090

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Document de travail / Working paper

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https://hal.archives-ouvertes.fr/hal-02908790

Date

2020

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Cahier de recherche CEREMADE

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Auteur(s)

Kazeykina, Anna
Laboratoire de Mathématiques d'Orsay [LMO]
Ren, Zhenjie
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Tan, Xiaolu
Department of mathematics, Chinese University of Hong Kong
Yang, Junjian
Fakultät für Mathematik [Wien]

Résumé (EN)

We study the long time behavior of an underdamped mean-field Langevin (MFL) equation , and provide a general convergence as well as an exponential convergence rate result under different conditions. The results on the MFL equation can be applied to study the convergence of the Hamiltonian gradient descent algorithm for the overparametrized optimization. We then provide a numerical example of the algorithm to train a generative adversarial networks (GAN).