Ergodicity of the underdamped mean-field Langevin dynamics
Probability
2023-11-28 v3 Machine Learning
Optimization and Control
Machine Learning
Abstract
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).
Keywords
Cite
@article{arxiv.2007.14660,
title = {Ergodicity of the underdamped mean-field Langevin dynamics},
author = {Anna Kazeykina and Zhenjie Ren and Xiaolu Tan and Junjian Yang},
journal= {arXiv preprint arXiv:2007.14660},
year = {2023}
}
Comments
45 pages, 9 figures