Quantitative convergence bounds for kinetic Langevin and Hamiltonian Monte Carlo

Monmarché Pierre, Sorbonne Université

Splitting schemes for the Hamiltonian and (underdamped) Langevin dynamics, which are kinetic (possibly non-reversible) processes, are widely used in Markov Chain Monte Carlo methods. We will present non-asymptotic efficiency bounds obtained in [1,2,3] for this family of MCMC samplers, under the assumption that the target measure satisfies a log-Sobolev inequality. The estimates are explicit and have a sharp dependency in the parameters of the problem (step-size, log-Sobolev constant, dimension...). The proof is based on a discrete-time adaptation of Villani’s modified entropy method. We will also discuss the dependency on the friction parameter in the case of Gaussian targets.

Area: CS35 - Monte Carlo methods and Applications I (Francesca R Crucinio, Alessandra Iacobucci, Andrea Bertazzi)

Keywords: Hamiltonian Monte Carlo ; underdamped Langevin diffusion ; log-Sobolev inequality ; hypocoercivity

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