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arXiv · 2205.10188

A Proximal Algorithm for Sampling from Non-convex Potentials

Jiaming Liang·Yongxin Chen
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Abstract

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.

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Jiaming Liang, Yongxin Chen. 2023-02-20. A Proximal Algorithm for Sampling from Non-convex Potentials. https://arxiv.org/abs/2205.10188

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