论文标题
改进了用于采样的近端算法的分析
Improved analysis for a proximal algorithm for sampling
论文作者
论文摘要
我们研究了Lee，Shen和Tian（2021）的近端采样器，并在假设较弱的假设下获得了新的收敛保证，而不是强烈的对数concavity：即，我们的结果适用于（1）（1）弱的对数conconcave目标，以及（2）允许不满意的假设，这些假设允许非log-log-conconconconconconconconconconcovity。我们通过为几类目标分布获得新的最先进的采样保证来证明我们的结果。我们还通过将近端采样器解释为熵正规化的瓦斯汀近端方法，而近端方法将近端采样器与近端方法解释为近端采样器的限制，从而加强了优化近端方法之间的联系。
We study the proximal sampler of Lee, Shen, and Tian (2021) and obtain new convergence guarantees under weaker assumptions than strong log-concavity: namely, our results hold for (1) weakly log-concave targets, and (2) targets satisfying isoperimetric assumptions which allow for non-log-concavity. We demonstrate our results by obtaining new state-of-the-art sampling guarantees for several classes of target distributions. We also strengthen the connection between the proximal sampler and the proximal method in optimization by interpreting the proximal sampler as an entropically regularized Wasserstein proximal method, and the proximal point method as the limit of the proximal sampler with vanishing noise.
