UNADJUSTED HAMILTONIAN MCMC WITH STRATIFIED MONTE CARLO TIME INTEGRATION

• 成果类型: Article
• 署名作者: Bou-rabee, Nawaf; Marsden, MILO.
• 署名单位: Rutgers University System; Rutgers University Camden; Rutgers University New Brunswick; Stanford University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2116
• 发表日期: 2025
• 页码: 360-392
• 关键词: convergence; ergodicity; algorithms

摘要

A randomized time integrator is suggested for unadjusted Hamiltonian Monte Carlo (uHMC) which involves a very minor modification to the usual Verlet time integrator, and hence, is easy to implement. For target distributions of the form mu(dx) proportional to e-U(x) dx where U : Rd -> R >= 0 is K-strongly convex but only L-gradient Lipschitz, and initial distributions epsilon with finite second moment, coupling proofs reveal that an epsilon-accurate approximation of the target distribution in L2-Wasserstein distance W2 can be achieved by the uHMC algorithm with randomized time integration using O((d/K)1/3(L/K)5/3 epsilon-2/3log(W2(mu, nu)/epsilon)+) gradient evaluations; whereas for such rough target densities the corresponding complexity of the uHMC algorithm with Verlet time integration is in general O((d/K)1/2(L/K)2 epsilon-1log(W2(mu,nu)/epsilon)+). Metropolis-adjustable randomized time integrators are also provided.