  We propose a fast stochastic Hamilton Monte Carlo (HMC) method, for sampling
from a smooth and strongly log-concave distribution. At the core of our
proposed method is a variance reduction technique inspired by the recent
advance in stochastic optimization. We show that, to achieve $\epsilon$
accuracy in 2-Wasserstein distance, our algorithm achieves $\tilde
O(n+\kappa^{2}d^{1/2}/\epsilon+\kappa^{4/3}d^{1/3}n^{2/3}/\epsilon^{2/3})$
gradient complexity (i.e., number of component gradient evaluations), which
outperforms the state-of-the-art HMC and stochastic gradient HMC methods in a
wide regime. We also extend our algorithm for sampling from smooth and general
log-concave distributions, and prove the corresponding gradient complexity as
well. Experiments on both synthetic and real data demonstrate the superior
performance of our algorithm.
