arXiv：cs.LG· Changwei Tu, Xiaoyu Wang, Yingli Wang, Xicheng Zhang, Lingjiong Zhu·· 4 小时前AI 评分33
反射锚定 Langevin 算法：面向非可微目标的约束采样方法 RALD 与 RALMC
Reflected Anchored Langevin Algorithms
AI 导读
该论文提出反射锚定 Langevin 动力学（RALD），一种在约束域上收敛至非可微目标的反射扩散过程，通过平滑锚定参考势并对漂移项与噪声协方差施加同一状态相关缩放因子实现。
正文
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.
| Comments: | 70 pages, 9 figures |
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG); Probability (math.PR) |
| Cite as: | arXiv:2610.09522 [stat.ML] |
| (or arXiv:2610.09522v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.09522 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Xiaoyu Wang [view email]
[v1]
Wed, 7 Oct 2026 06:16:49 UTC (3,420 KB)
来源：arXiv：cs.LG · arxiv.org