Variance Reduction using Nonreversible Langevin Samplers

TL;DR

This paper investigates how adding a nonreversible component to Langevin samplers reduces variance and accelerates convergence, supported by theoretical analysis and numerical experiments.

Contribution

It provides a detailed analysis of how nonreversibility affects asymptotic variance in Langevin samplers, with theoretical and numerical insights.

Findings

Nonreversible Langevin dynamics reduce asymptotic variance.

Nonreversibility speeds up convergence to the target distribution.

Theoretical results are confirmed by numerical simulations.

Abstract

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.