PRJul 29, 2020
Ergodicity of the underdamped mean-field Langevin dynamicsAnna Kazeykina, Zhenjie Ren, Xiaolu Tan et al.
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).