Kazeykina, A., Ren, Z., Tan, X., & Yang, J. (2024). Ergodicity of the underdamped mean-field Langevin dynamics. Annals of Applied Probability, 34(3), 3181–3226. https://doi.org/10.1214/23-AAP2036
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 some numerical examples of the algorithm to train a generative adversarial network (GAN).
en
Research Areas:
Mathematical Methods in Economics: 50% Fundamental Mathematics Research: 50%
