标题： 改进可逆采样器的收敛性 显示英文标题

标题： Improving the convergence of reversible samplers

摘要： 在蒙特卡洛方法中，用于采样给定目标分布的马尔可夫过程通常满足细致平衡，即它们是时间可逆的。然而，相对较新的结果表明，适当的可逆和不可逆扰动可以加速收敛到平衡状态。在本文中，我们提出了一些适用于一般马尔可夫过程的一般设计原则。通过与马尔可夫过程的生成器一起工作，我们证明对于一些最常用的表现准则，即谱隙、渐近方差和大偏差泛函，对于某些初始可逆采样器的适当可逆和不可逆扰动，采样得到了改进。此外，我们为各种常用的马尔可夫过程，如马尔可夫链和扩散过程，提供了此类可逆和不可逆扰动的具体构造。在扩散过程的情况下，我们使用大偏差率函数作为性能度量，使讨论更加具体。 显示英文摘要

摘要： In Monte-Carlo methods the Markov processes used to sample a given target distribution usually satisfy detailed balance, i.e. they are time-reversible. However, relatively recent results have demonstrated that appropriate reversible and irreversible perturbations can accelerate convergence to equilibrium. In this paper we present some general design principles which apply to general Markov processes. Working with the generator of Markov processes, we prove that for some of the most commonly used performance criteria, i.e., spectral gap, asymptotic variance and large deviation functionals, sampling is improved for appropriate reversible and irreversible perturbations of some initially given reversible sampler. Moreover we provide specific constructions for such reversible and irreversible perturbations for various commonly used Markov processes, such as Markov chains and diffusions. In the case of diffusions, we make the discussion more specific using the large deviations rate function as a measure of performance.