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.
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Cite this article
APA 7
Tu, C., Wang, X., Wang, Y., Zhang, X., & Zhu, L. (2026). Reflected Anchored Langevin Algorithms. https://omanscience.com/en/articles/reflected-anchored-langevin-algorithms
MLA 9
Tu, Changwei, et al. "Reflected Anchored Langevin Algorithms." https://omanscience.com/en/articles/reflected-anchored-langevin-algorithms.
Chicago (author–date)
Tu, Changwei, Xiaoyu Wang, Yingli Wang, Xicheng Zhang, and Lingjiong Zhu. 2026. "Reflected Anchored Langevin Algorithms." https://omanscience.com/en/articles/reflected-anchored-langevin-algorithms.
Harvard
Tu, C., Wang, X., Wang, Y., Zhang, X. and Zhu, L. (2026) 'Reflected Anchored Langevin Algorithms', Available at: https://omanscience.com/en/articles/reflected-anchored-langevin-algorithms.
Vancouver
Tu C, Wang X, Wang Y, Zhang X, Zhu L. Reflected Anchored Langevin Algorithms. https://omanscience.com/en/articles/reflected-anchored-langevin-algorithms
IEEE
C. Tu, X. Wang, Y. Wang, X. Zhang, and L. Zhu, "Reflected Anchored Langevin Algorithms," https://omanscience.com/en/articles/reflected-anchored-langevin-algorithms.