Mangoubi, OrenSmith, Aaron2020-03-062020-03-062020-03-062019-01-01https://infoscience.epfl.ch/handle/20.500.14299/167066WOS:000509687900061We 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.convergenceequilibriumlangevinperturbationalgorithmtrendtext::conference output::conference proceedings::conference paper