论文标题
来自非凸电势采样的近端算法
A Proximal Algorithm for Sampling from Non-convex Potentials
论文作者
论文摘要
我们研究与缺乏平滑度的非凸电势相关的采样问题。特别是，我们考虑满足对数 - 贝贝尔的不平等或庞加莱不平等的目标分布。假定电势是半平滑的，或者是多个半平滑函数的总和。我们开发了一种采样算法，该算法类似于针对此具有挑战性的抽样任务的优化近端算法。我们的算法基于一种被称为交替采样框架（ASF）的吉布斯采样的特殊情况。这项工作的关键贡献是基于非凸和半平滑设置中的拒绝采样的实现ASF的实际实现。这项工作将\ cite {liache21，liache22}的最新算法扩展到具有非convex电位的非平滑/半平滑log-conconcave分布到设置。在这项工作中几乎所有采样的情况下，我们的近端采样算法都比所有现有方法都能达到更好的复杂性。
We study sampling problems associated with non-convex potentials that meanwhile lack smoothness. In particular, we consider target distributions that satisfy either logarithmic-Sobolev inequality or Poincaré inequality. Rather than smooth, the potentials are assumed to be semi-smooth or the summation of multiple semi-smooth 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 in the non-convex and semi-smooth setting. This work extends the recent algorithm in \cite{LiaChe21,LiaChe22} for non-smooth/semi-smooth log-concave distribution to the setting with non-convex potentials. In almost all the cases of sampling considered in this work, our proximal sampling algorithm achieves better complexity than all existing methods.
