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Ergodicity of the underdamped mean-field Langevin dynamics

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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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02908790
Date
2020
Series title
Cahier de recherche CEREMADE
Pages
29
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Author(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]
Abstract (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).
Subjects / Keywords
mean-field Langevin dynamics