Is There an Analog of Nesterov Acceleration for MCMC?
Machine Learning
2019-10-23 v2 Machine Learning
Numerical Analysis
Numerical Analysis
Abstract
We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective functional. We show that an underdamped form of the Langevin algorithm performs accelerated gradient descent in this metric. To characterize the convergence of the algorithm, we construct a Lyapunov functional and exploit hypocoercivity of the underdamped Langevin algorithm. As an application, we show that accelerated rates can be obtained for a class of nonconvex functions with the Langevin algorithm.
Keywords
Cite
@article{arxiv.1902.00996,
title = {Is There an Analog of Nesterov Acceleration for MCMC?},
author = {Yi-An Ma and Niladri Chatterji and Xiang Cheng and Nicolas Flammarion and Peter Bartlett and Michael I. Jordan},
journal= {arXiv preprint arXiv:1902.00996},
year = {2019}
}