We study sampling problems associated with potentials that lack smoothness. The potentials can be either convex or non-convex. Departing from the standard smooth setting, the potentials are only assumed to be weakly smooth or non-smooth, or the summation of multiple such functions. We develop a sampling algorithm that resembles proximal algorithms in optimization for this challenging sampling task. Our algorithm is based on a special case of Gibbs sampling known as the alternating sampling framework (ASF). The key contribution of this work is a practical realization of the ASF based on rejection sampling for both non-convex and convex potentials that are not necessarily smooth. In almost all the cases of sampling considered in this work, our proximal sampling algorithm achieves better complexity than all existing methods.

翻译：本文研究了与缺乏光滑性的势函数相关的抽样问题。这些势函数可以是凸函数或非凸函数。与标准光滑设置不同，本文假设势函数仅为弱光滑、非光滑，或是多个此类函数之和。针对这一具有挑战性的抽样任务，我们提出了一种类似于优化中近端算法的抽样算法。该算法基于吉布斯采样的特例——交替抽样框架（ASF）。本文的关键贡献在于，基于拒绝抽样方法，针对不一定光滑的非凸和凸势函数，实现了ASF的实际应用。在本文所考虑的大多数抽样情形中，我们的近端抽样算法较所有现有方法具有更优的复杂度。