Variance Reduction using Nonreversible Langevin Samplers
For researchers using Markov chain Monte Carlo methods, it provides theoretical understanding of variance reduction via nonreversibility.
The paper studies how adding a nonreversible component to Langevin dynamics reduces the asymptotic variance of time-averaging estimators for expectations under a target distribution, supported by numerical simulations.
A standard approach to computing expectations with respect to a given target measure is to introduce an overdamped Langevin equation which is reversible with respect to the target distribution, and to approximate the expectation by a time-averaging estimator. As has been noted in recent papers, introducing an appropriately chosen nonreversible component to the dynamics is beneficial, both in terms of reducing the asymptotic variance and of speeding up convergence to the target distribution. In this paper we present a detailed study of the dependence of the asymptotic variance on the deviation from reversibility. Our theoretical findings are supported by numerical simulations.