Efficiently handling constraints with Metropolis-adjusted Langevin algorithm
This addresses a challenge in Markov chain Monte Carlo methods for constrained distributions, but appears incremental as it builds on existing algorithms.
The study tackled the problem of applying the Metropolis-adjusted Langevin algorithm to constrained target distributions, showing it is highly effective with a superior mixing time bound compared to competing algorithms without an accept-reject step.
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.