In this paper, we explore sampling from strongly log-concave distributions defined on convex and compact supports. We propose a general proximal framework that involves projecting onto the constrained set, which is highly flexible and supports various projection options. Specifically, we consider the cases of Euclidean and Gauge projections, with the latter having the advantage of being performed efficiently using a membership oracle. This framework can be seamlessly integrated with multiple sampling methods. Our analysis focuses on Langevin-type sampling algorithms within the context of constrained sampling. We provide nonasymptotic upper bounds on the W1 and W2 errors, offering a detailed comparison of the performance of these methods in constrained sampling.

翻译：本文研究了定义在凸紧支撑集上的强对数凹分布采样问题。我们提出了一种通用的近端框架，该框架涉及对约束集的投影操作，具有高度灵活性并支持多种投影选项。具体而言，我们考虑了欧几里得投影和规范投影两种情况，其中后者具有可通过成员资格预言机高效执行的优点。该框架可与多种采样方法无缝集成。我们的分析聚焦于约束采样背景下的朗之万型采样算法。我们给出了W1和W2误差的非渐近上界，并对这些方法在约束采样中的性能进行了详细比较。