  Stochastic gradient Hamiltonian Monte Carlo (SGHMC) is an efficient method
for sampling from continuous distributions. It is a faster alternative to HMC:
instead of using the whole dataset at each iteration, SGHMC uses only a
subsample. This improves performance, but introduces bias that can cause SGHMC
to converge to the wrong distribution. One can prevent this using a step size
that decays to zero, but such a step size schedule can drastically slow down
convergence. To address this tension, we propose a novel second-order SG-MCMC
algorithm---AMAGOLD---that infrequently uses Metropolis-Hastings (M-H)
corrections to remove bias. The infrequency of corrections amortizes their
cost. We prove AMAGOLD converges to the target distribution with a fixed,
rather than a diminishing, step size, and that its convergence rate is at most
a constant factor slower than a full-batch baseline. We empirically demonstrate
AMAGOLD's effectiveness on synthetic distributions, Bayesian logistic
regression, and Bayesian neural networks.
