In this paper, we propose a novel class of Piecewise Deterministic Markov Processes (PDMPs) that are designed to sample from probability distributions $π$ supported on a convex set $\mathcal{M}$. This class of PDMPs adapts the concept of a mirror map from convex optimisation to address sampling problems. The corresponding algorithms provide unbiased samples that respect the constraints and, moreover, allow for exact subsampling. We demonstrate the advantages of these algorithms against a range of constrained sampling problems where the proposed algorithms outperform state of the art stochastic differential equation-based methods.

翻译：本文提出了一类新型分段确定性马尔可夫过程（PDMP），旨在从支撑在凸集 $\mathcal{M}$ 上的概率分布 $\pi$ 中进行采样。该类 PDMP 借鉴了凸优化中的镜像映射概念，用于解决采样问题。相应算法可提供无偏样本，且样本严格满足约束条件，并支持精确子采样。我们在多个约束采样问题上展示了这些算法的优势，证明所提方法在性能上优于当前最先进的基于随机微分方程的方法。