On explicit $L^2$-convergence rate estimate for piecewise deterministic Markov processes in MCMC algorithms

Abstract

We establish $L^2$-exponential convergence rate for three popular piecewise deterministic Markov processes for sampling: the randomized Hamiltonian Monte Carlo method, the zigzag process, and the bouncy particle sampler. Our analysis is based on a variational framework for hypocoercivity, which combines a Poincaré-type inequality in time-augmented state space and a standard $L^2$ energy estimate. Our analysis provides explicit convergence rate estimates, which are more quantitative than existing results.

Under minor revision

References in corpus (2)

• Hypocoercivity and exponential time decay for the linear inhomogeneous relaxation Boltzmann equation
• Generalized Bouncy Particle Sampler

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• Weighted $L^2$-contractivity of Langevin dynamics with singular potentials
• Birth-death dynamics for sampling: Global convergence, approximations and their asymptotics
• Complexity of zigzag sampling algorithm for strongly log-concave distributions
• Non-reversible lifts of reversible diffusion processes and relaxation times
• Unadjusted Hamiltonian MCMC with Stratified Monte Carlo Time Integration
• Bosonized one-dimensional quantum systems through enhanced event-chain Monte Carlo
• An entropic approach for Hamiltonian Monte Carlo: the idealized case
• Hypocoercivity meets lifts