Mixing time guarantees for unadjusted Hamiltonian Monte Carlo

We provide quantitative upper bounds on the total variation mixing time of Markov chain corresponding to unadjusted Hamiltonian Monte Carlo (uHMC) algorithm. For two general classes models and fixed discretization step size h, is shown depend only logarithmically dimension. Moreover, we distance between invariant measure uHMC true target measure. As a consequence, show that an ε-accurate approximation distribution μ in can be achieved by uHMC: (i) for broad class with Od3∕4ε−1∕2log(d∕ε) gradient evaluations; (ii) mean field weak interactions Od1∕2ε−1∕2log(d∕ε) evaluations. The proofs are based construction successful couplings realize bounds.