In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a polynomial-time complexity $\tilde {\cal O}(d\varepsilon^{-1})$ to obtain $\varepsilon$ total variation distance to the target density, better than most existing results under the same assumptions. Our method is based on the proximal bundle method and an alternating sampling framework. This framework requires the so-called restricted Gaussian oracle, which can be viewed as a sampling counterpart of the proximal mapping in convex optimization. One key contribution of this work is a fast algorithm that realizes the restricted Gaussian oracle for any convex non-smooth potential with bounded Lipschitz constant.

翻译：在这项工作中,我们研究非悬浮潜力的抽样问题。 我们提出一个新的Markov连锁Monte Carlo算法,用于从非悬浮潜力进行抽样。 我们对我们的算法进行非被动分析,并建立一个多元时间复杂性$\tilde {cal O}(d\d\varepsilon}-1})$,以获得与目标密度的总差异距离,比同一假设下的大多数现有结果要好。 我们的方法基于准氧化捆绑法和一个交替抽样框架。 这个框架需要所谓的限制高须符, 它可以被视为曲线优化中准X映像的抽样对应方。 这项工作的一个关键贡献是快速算法, 它可以实现与连接的 Lipschitz 恒定线的任何二次曲线的非移动潜力的受限高司或触动。