改进了无调整Langevin算法的收敛速度，更精确估计误差。
Wasserstein mixing time of the unadjusted Langevin algorithm
- 基于Wasserstein距离分析算法渐近偏差
- 混合时间达到κ√d/ε，提升√d/ε倍
- 适合关注采样算法精度的研究者
本文针对对数光滑且强对数凹测度的经典情形，提供了无调整Langevin算法在Wasserstein距离下的新偏差估计。该界表明，算法的Wasserstein混合时间为O(κ√d/ε)，其中κ为条件数，d为维度，ε为目标精度。相比此前最优结果，该界提升了√d/ε倍，显著优化了收敛速率。
原文摘要 · Abstract (English)
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.
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