发表机构
Section de Mathématiques, Université de Genève; Department of Mathematics, Imperial College（日内瓦大学数学系; 帝国理工学院数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出通过添加可逆Stratonovich扰动加速过阻尼Langevin动力学收敛至平衡，证明高斯目标下的最优缩放并给出构造算法，数值实验显示其超越二次情形的效率。
AI 中文摘要
本文研究了利用Langevin型动力学从概率分布中采样的问题。我们考虑过阻尼Langevin动力学，通过添加保持可逆性的Stratonovich扰动来对其进行扰动。我们证明了应用于高斯目标分布的Stratonovich扰动的最优缩放，并推导出一种构造此类扰动的算法。我们的理论结果辅以数值实验，在实验中我们将所提方法与不可逆采样器及过阻尼Langevin动力学进行了比较。数值实验证明了该方法在二次情形之外的效率。
英文摘要
In this paper, we study the problem of sampling from a probability distribution using Langevin-type dynamics. We consider overdamped Langevin dynamics perturbed by adding a Stratonovich perturbation that preserves reversibility. We prove an optimal scaling for the Stratonovich perturbation applied to Gaussian target distributions and derive an algorithm to construct such perturbation. Our theoretical results are supplemented by numerical experiments in which we compare our proposed method with nonreversible samplers and overdamped Langevin dynamics. Our numerical experiments demonstrate the efficiency of the approach beyond the quadratic case.
