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Ergodicity of the underdamped mean-field Langevin dynamics (2007.14660v3)

Published 29 Jul 2020 in math.PR, cs.LG, math.OC, and stat.ML

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).

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