AMAGOLD: Amortized Metropolis Adjustment for Efficient Stochastic Gradient MCMC

• URL: http://arxiv.org/abs/2003.00193v1
• Date: Sat, 29 Feb 2020 06:57:43 GMT
• Title: AMAGOLD: Amortized Metropolis Adjustment for Efficient Stochastic Gradient MCMC
• Authors: Ruqi Zhang, A. Feder Cooper, Christopher De Sa
• Abstract summary: Hamiltonian Monte Carlo (SGHMC) is an efficient method for sampling from continuous distributions. We propose a novel second-order SG-MCMC algorithm---AMAGOLD---that infrequently uses Metropolis-Hastings (M-H) corrections to remove bias. 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.
• Score: 37.768023232677244
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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