Mixing of Hamiltonian Monte Carlo on strongly log-concave distributions 2: Numerical integrators


Oren Mangoubi, Aaron Smith ;
Proceedings of Machine Learning Research, PMLR 89:586-595, 2019.


We obtain quantitative bounds on the mixing properties of the Hamiltonian Monte Carlo (HMC) algorithm with target distribution in d-dimensional Euclidean space, showing that HMC mixes quickly whenever the target log-distribution is strongly concave and has Lipschitz gradients. We use a coupling argument to show that the popular leapfrog implementation of HMC can sample approximately from the target distribution in a number of gradient evaluations which grows like d^1/2 with the dimension and grows at most polynomially in the strong convexity and Lipschitz-gradient constants. Our results significantly extend and improve on the dimension dependence of previous quantitative bounds on the mixing of HMC and of the unadjusted Langevin algorithm in this setting.

Related Material