Efficiently handling constraints with Metropolis-adjusted Langevin algorithm

Jinyuan Chang; Cheng Yong Tang; Yuanzheng Zhu

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arXiv · 2302.11971

Efficiently handling constraints with Metropolis-adjusted Langevin algorithm

Jinyuan Chang·Cheng Yong Tang·Yuanzheng Zhu

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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.

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Jinyuan Chang, Cheng Yong Tang, Yuanzheng Zhu. 2023-02-23. Efficiently handling constraints with Metropolis-adjusted Langevin algorithm. https://arxiv.org/abs/2302.11971

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