Using Perturbed Underdamped Langevin Dynamics to Efficiently Sample from Probability Distributions
This work provides a theoretical framework for improving Langevin samplers, which is relevant for practitioners in computational statistics and machine learning who need efficient sampling from probability distributions.
The authors introduce perturbed underdamped Langevin dynamics that preserve the invariant measure of the standard dynamics, and show that appropriate perturbations reduce asymptotic variance, with theoretical analysis for Gaussian targets and numerical validation for non-Gaussian targets.
In this paper we introduce and analyse Langevin samplers that consist of perturbations of the standard underdamped Langevin dynamics. The perturbed dynamics is such that its invariant measure is the same as that of the unperturbed dynamics. We show that appropriate choices of the perturbations can lead to samplers that have improved properties, at least in terms of reducing the asymptotic variance. We present a detailed analysis of the new Langevin sampler for Gaussian target distributions. Our theoretical results are supported by numerical experiments with non-Gaussian target measures.