An entropic approach for Hamiltonian Monte Carlo: the idealized case
Abstract
Quantitative long-time entropic convergence and short-time regularization are established for an idealized Hamiltonian Monte Carlo chain which alternatively follows an Hamiltonian dynamics for a fixed time and then partially or totally refreshes its velocity with an auto-regressive Gaussian step. These results, in discrete time, are the analogous of similar results for the continuous-time kinetic Langevin diffusion, and the latter can be obtained from our bounds in a suitable limit regime. The dependency in the log-Sobolev constant of the target measure is sharp and is illustrated on a mean-field case and on a low-temperature regime, with an application to the simulated annealing algorithm. The practical unadjusted algorithm is briefly discussed.
Keywords
Cite
@article{arxiv.2209.13405,
title = {An entropic approach for Hamiltonian Monte Carlo: the idealized case},
author = {Pierre Monmarché},
journal= {arXiv preprint arXiv:2209.13405},
year = {2023}
}