Ergodicity of the underdamped mean-field Langevin dynamics
arXiv:2007.14660
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).
45 pages, 9 figures
References in corpus (5)
- Underdamped Langevin MCMC: A non-asymptotic analysis
- A Mean-field Analysis of Deep ResNet and Beyond: Towards Provable Optimization Via Overparameterization From Depth
- Mean-Field Neural ODEs via Relaxed Optimal Control
- Mean-field Langevin System, Optimal Control and Deep Neural Networks
- The Kinetic Fokker-planck Equation With Mean Field Interaction