Two-scale coupling for preconditioned Hamiltonian Monte Carlo in infinite dimensions

Abstract

We derive non-asymptotic quantitative bounds for convergence to equilibrium of the exact preconditioned Hamiltonian Monte Carlo algorithm (pHMC) on a Hilbert space. As a consequence, explicit and dimension-free bounds for pHMC applied to high-dimensional distributions arising in transition path sampling and path integral molecular dynamics are given. Global convexity of the underlying potential energies is not required. Our results are based on a two-scale coupling which is contractive in a carefully designed distance.

arXiv comment36 pages, 4 figures

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• Mixing of Metropolis-Adjusted Markov Chains via Couplings: The High Acceptance Regime