Ergodicity of the underdamped mean-field Langevin dynamics

Understand

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).