Work

Reflected Anchored Langevin Algorithms

Year: 2026

Type: preprint

Abstract: First order Langevin algorithms for constrained sampling in machine learning, such as projected Langevin Monte Carlo which are based on discretizations of reflected Langevin dynamics, require differentiable log densities that limits their applicability. This paper introduces reflected anchored Langevin dynamics (RALD), a reflected diffusion that converges to non-differentiable targets on constrained domains. The method uses a smooth anchored reference potential and multiplies the drift and noise covariance of its reflected Langevin dynamics by the same state dependent scaling factor. Its Euler-Maruyama discretization with projection gives reflected anchored Langevin Monte Carlo (RALMC) algorithm. We prove explicit convergence bounds and iteration complexity for RALMC in the 2-Wasserstein distance to the target distribution. Numerical experiments are provided to illustrate the theoretical predictions and the empirical performance of the method.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.09522

Authors: Tu, Changwei, Wang, Xiaoyu, Wang, Yingli, Zhang, Xicheng, Zhu, Lingjiong

Institutions: The Hong Kong University of Science and Technology (Guangzhou), Fudan University, Beijing Institute of Technology, Florida State University

Language: English

Topic: Markov Chains and Monte Carlo Methods

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Hong Kong University of Science and Technology

Award: G6767698131

OpenAlex ID: W7220891870

Cites: 6

Cited by: 2

Related to: 10