发表机构
ETH Zürich（苏黎世联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对对数强凹测度场景，推导了未校准朗之万算法的Wasserstein混合时间界，将其量级定为κ√d/ε，较此前最优结果实现了√d/ε倍的性能提升。
AI 中文摘要
针对对数强凹测度的经典场景，我们对未校准朗之万算法的渐近偏差给出了Wasserstein距离的新估计。所得界表明Wasserstein混合时间为κ√d/ε量级，其中κ为条件数、d为维度、ε为目标精度；该结果较此前最优结果提升了√d/ε倍。
英文摘要
We provide new estimates in Wasserstein distance for the asymptotic bias of the unadjusted Langevin algorithm, in the classical setting of log-smooth strongly log-concave measures. Our bound implies a Wasserstein mixing time of order $κ\sqrt{d}/\varepsilon$, where $κ$ is the condition number, $d$ is the dimension, and $\varepsilon$ is the target precision: this improves by a factor of $\sqrt{d}/\varepsilon$ over the previous state-of-the-art results.
Comments8 pages
