论文标题
使用过度引导的langevin算法进行采样的前向信封
The Forward-Backward Envelope for Sampling with the Overdamped Langevin Algorithm
论文作者
论文摘要
在本文中，我们基于向前倾斜分裂的概念来分析一种近端方法，以从不一定光滑的分布中进行采样。特别是，我们研究了Langevin方程的Euler-Maruyama离散化的非质子性特性，其中使用前向信封来处理动力学的非平滑部分。与广泛使用的Moreu-Yoshida One和Myula算法相比，该信封的一个优点是它维护原始非平滑分布的地图估计器。我们还研究了许多支持我们理论发现的数值实验。
In this paper, we analyse a proximal method based on the idea of forward-backward splitting for sampling from distributions with densities that are not necessarily smooth. In particular, we study the non-asymptotic properties of the Euler-Maruyama discretization of the Langevin equation, where the forward-backward envelope is used to deal with the non-smooth part of the dynamics. An advantage of this envelope, when compared to widely-used Moreu-Yoshida one and the MYULA algorithm, is that it maintains the MAP estimator of the original non-smooth distribution. We also study a number of numerical experiments that corroborate that support our theoretical findings.
