Sampling with Shielded Langevin Monte Carlo Using Navigation Potentials

TL;DR

This paper presents a novel constrained sampling method called shielded Langevin Monte Carlo that effectively samples from complex, punctured spaces by combining adaptive temperature and repulsive drift, demonstrated on Gaussian mixtures and MIMO detection.

Contribution

The paper introduces a new constrained sampling algorithm inspired by navigation functions, capable of handling non-convex spaces with convex holes, which was previously challenging.

Findings

Effective sampling in punctured, non-convex spaces demonstrated.

Outperforms unconstrained Langevin Monte Carlo in constrained scenarios.

Applicable to complex distributions like Gaussian mixtures and MIMO detection.

Abstract

We introduce shielded Langevin Monte Carlo (LMC), a constrained sampler inspired by navigation functions, capable of sampling from unnormalized target distributions defined over punctured supports. In other words, this approach samples from non-convex spaces defined as convex sets with convex holes. This defines a novel and challenging problem in constrained sampling. To do so, the sampler incorporates a combination of a spatially adaptive temperature and a repulsive drift to ensure that samples remain within the feasible region. Experiments on a 2D Gaussian mixture and multiple-input multiple-output (MIMO) symbol detection showcase the advantages of the proposed shielded LMC in contrast to unconstrained cases.