Efficiently handling constraints with Metropolis-adjusted Langevin algorithm

TL;DR

This paper analyzes the Metropolis-adjusted Langevin algorithm's efficiency in constrained settings, providing theoretical convergence guarantees and demonstrating superior mixing time bounds compared to other algorithms, supported by numerical experiments.

Contribution

It offers a rigorous analysis of the algorithm's convergence and mixing time bounds in constrained support scenarios, highlighting its effectiveness over existing methods.

Findings

The algorithm converges with proven mixing time bounds.

It outperforms competing algorithms without accept-reject steps.

Numerical experiments confirm theoretical advantages.

Abstract

In this study, we investigate the performance of the Metropolis-adjusted Langevin algorithm in a setting with constraints on the support of the target distribution. We provide a rigorous analysis of the resulting Markov chain, establishing its convergence and deriving an upper bound for its mixing time. Our results demonstrate that the Metropolis-adjusted Langevin algorithm is highly effective in handling this challenging situation: the mixing time bound we obtain is superior to the best known bounds for competing algorithms without an accept-reject step. Our numerical experiments support these theoretical findings, indicating that the Metropolis-adjusted Langevin algorithm shows promising performance when dealing with constraints on the support of the target distribution.