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Dec, 2020
Metropolis-Adjusted Langevin算法的最优维度依赖
Optimal dimension dependence of the Metropolis-Adjusted Langevin Algorithm
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Sinho Chewi, Chen Lu, Kwangjun Ahn, Xiang Cheng, Thibaut Le Gouic...
TL;DR
该文研究了非渐近情况下，基于新的技术 ─ Metropolis调整的投影特征，将MALA算法的分析简化到Langevin SDE分析领域，从而证明了在一定条件下，MALA算法得到的混合时间为O(d^(1/2))
Abstract
Conventional wisdom in the sampling literature, backed by a popular diffusion scaling limit, suggests that the
mixing time
of the
metropolis-adjusted langevin algorithm
(MALA) scales as $O(d^{1/3})$, where $d$ is
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