提出非可逆约束采样新方法，收敛更快更稳定。
Non-Reversible Langevin Algorithms for Constrained Sampling
- 引入偏斜反射机制的非可逆朗之万动态，打破对称性提升效率。
- 理论证明在总变差与1-Wasserstein距离下均有非渐近收敛速率。
- 适用于需高效精确采样的高维约束问题，如物理模拟与贝叶斯推断。
我们研究约束域上的目标分布采样问题。提出一种连续时间随机微分方程——偏斜反射非可逆朗之万动力学（SRNLD），其具有偏斜反射边界。在总变差和1-Wasserstein距离下，获得了SRNLD到目标分布的非渐近收敛速率。通过破坏可逆性，证明其收敛速度优于可逆动力学的特例。基于SRNLD的离散化，提出偏斜反射非可逆朗之万蒙特卡洛（SRNLMC），并获得从SRNLD到离散算法的非渐近误差界，以及在1-Wasserstein距离下的目标分布收敛保证。相比基于可逆动力学的投影朗之万蒙特卡洛，性能保证更优。在合成数据与真实数据上进行了数值实验，验证了所提算法的高效性。
原文摘要 · Abstract (English)
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.
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