机器学习与数据科学博士生系列论坛（第一百零七期）—— From Langevin Dynamics to Nonsmooth Sampling: Recent Advances in the Analysis of MYULA
Holder： Yuchen Xin（Peking University）
Time：2026-10-08 16:00-17:00
Location：Tencent Conference 441-3293-3791
Abstract:
Sampling from probability distributions is a fundamental task in statistics and machine learning. Langevin methods combine gradient information with random noise, but models with nonsmooth penalties present additional challenges. A standard approach is to smooth the nonsmooth component and then apply Langevin updates, as in the Moreau–Yosida unadjusted Langevin algorithm (MYULA). This introduces a tradeoff: reducing the smoothing error makes the resulting dynamics more difficult to discretize accurately.
In this talk, we review the basic ideas of Langevin sampling and discuss recent advances in the analysis of MYULA. We explain how sharper guarantees emerge from accounting for how often regions of high curvature are visited, exploiting cancellations in discretization errors, and directly analyzing the algorithm's long-run distribution. For a class of strongly log-concave targets with convex Lipschitz penalties, the resulting iteration bounds have nearly linear dependence on inverse Wasserstein error tolerance, with model parameters held fixed.
About the Speaker:
该线上论坛每两周主办一次（除了公共假期）。论坛每次邀请一位博士生就某个前沿课题做较为系统深入的介绍，主题包括但不限于机器学习、高维统计学、运筹优化和理论计算机科学。
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