Non-Reversible Langevin Algorithms for Constrained Sampling
This addresses the problem of efficient sampling from constrained distributions for researchers and practitioners in machine learning and statistics, representing an incremental improvement over existing reversible Langevin algorithms.
The paper tackles the constrained sampling problem by proposing skew-reflected non-reversible Langevin dynamics (SRNLD) and its discretization (SRNLMC), achieving faster convergence rates than reversible methods in total variation and 1-Wasserstein distances.
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.