Efficiently handling constraints with Metropolis-adjusted Langevin algorithm
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.
Cite
@article{arxiv.2302.11971,
title = {Efficiently handling constraints with Metropolis-adjusted Langevin algorithm},
author = {Jinyuan Chang and Cheng Yong Tang and Yuanzheng Zhu},
journal= {arXiv preprint arXiv:2302.11971},
year = {2023}
}
Comments
We find some error in the proof of Theorem 2 and the associated result may not be correct