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Pré-Publication, Document De Travail Année : 2022

An entropic approach for Hamiltonian Monte Carlo: the idealized case

Pierre Monmarché

Résumé

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 refresh 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.

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hal-03873044 , version 1 (26-11-2022)

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Pierre Monmarché. An entropic approach for Hamiltonian Monte Carlo: the idealized case. 2022. ⟨hal-03873044⟩
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