Non-Reversible Langevin Algorithms for Constrained Sampling

Fuente: arXiv
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Main Authors: Du, Hengrong, Feng, Qi, Tu, Changwei, Wang, Xiaoyu, Zhu, Lingjiong
Format: Preprint
Published: 2025
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author Du, Hengrong
Feng, Qi
Tu, Changwei
Wang, Xiaoyu
Zhu, Lingjiong
author_facet Du, Hengrong
Feng, Qi
Tu, Changwei
Wang, Xiaoyu
Zhu, Lingjiong
contents We consider the constrained sampling problem where the goal is to sample from a target distribution on a constrained domain. We propose skew-reflected non-reversible Langevin dynamics (SRNLD), a continuous-time stochastic differential equation with skew-reflected boundary. We obtain non-asymptotic convergence rate of SRNLD to the target distribution in both total variation and 1-Wasserstein distances. By breaking reversibility, we show that the convergence is faster than the special case of the reversible dynamics. Based on the discretization of SRNLD, we propose skew-reflected non-reversible Langevin Monte Carlo (SRNLMC), and obtain non-asymptotic discretization error from SRNLD, and convergence guarantees to the target distribution in 1-Wasserstein distance. We show better performance guarantees than the projected Langevin Monte Carlo in the literature that is based on the reversible dynamics. Numerical experiments are provided for both synthetic and real datasets to show efficiency of the proposed algorithms.
format Preprint
id arxiv_https___arxiv_org_abs_2501_11743
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Non-Reversible Langevin Algorithms for Constrained Sampling
Du, Hengrong
Feng, Qi
Tu, Changwei
Wang, Xiaoyu
Zhu, Lingjiong
Machine Learning
Probability
Computation
We consider the constrained sampling problem where the goal is to sample from a target distribution on a constrained domain. We propose skew-reflected non-reversible Langevin dynamics (SRNLD), a continuous-time stochastic differential equation with skew-reflected boundary. We obtain non-asymptotic convergence rate of SRNLD to the target distribution in both total variation and 1-Wasserstein distances. By breaking reversibility, we show that the convergence is faster than the special case of the reversible dynamics. Based on the discretization of SRNLD, we propose skew-reflected non-reversible Langevin Monte Carlo (SRNLMC), and obtain non-asymptotic discretization error from SRNLD, and convergence guarantees to the target distribution in 1-Wasserstein distance. We show better performance guarantees than the projected Langevin Monte Carlo in the literature that is based on the reversible dynamics. Numerical experiments are provided for both synthetic and real datasets to show efficiency of the proposed algorithms.
title Non-Reversible Langevin Algorithms for Constrained Sampling
topic Machine Learning
Probability
Computation
url https://arxiv.org/abs/2501.11743