摘要：We study the Hamiltonian Monte Carlo (HMC) algorithm for sampling froma strongly logconcave density proportional to e-5 where f :Rd→Ris u-strong lyconvex and L-smooth (the condition number is K = L/u). Weshow that the relaxation time (inverse of the spectral gap) of ideal HMC is O(x), improving on the previous best bound of O(x1.5)(Lee et al., 2018); we complement this with an example wherethe relaxation time is Q(x), for any step-size. When implemented with an ODEsolver,HMC returns an e-approximate point in 2-Wasserstein distance using o(xd)0.5e-1)gradient evaluations per step and o((Kd)1 .5-1) total time.
关键词：logconcave distribution;sampling;Hamiltonian Monte Carlo;spectral gap;strong convexity
