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Quantitative convergence bounds for unadjusted kinetic Langevin and Hamiltonian Monte Carlo

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SSDW04 - Monte Carlo sampling: beyond the diffusive regime

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 discuss how, for Gaussian distributions, a very precise optimization of the parameters can be conducted, revealing how inertia induces a diffusive-to-ballistic speed-up for ill-conditioned targets. Motivated by this, we will present non-asymptotic efficiency bounds for this family of MCMC samplers that cover non-convex potentials and mean-field interacting particles.

This talk is part of the Isaac Newton Institute Seminar Series series.

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