A new generation of stochastic algorithms for sampling and optimization

在合适的梯度规则假设下，新一代随机梯度体面算法可以有效地找到可能复杂的高维景观的全局最小值。这种算法的收敛性分析与研究一类特殊的随机微分方程（SDEs）的遍历性质有关，即所谓的Langevin SDEs。本项目的主要重点是研究这类SDEs和结果算法的非渐近收敛分析，并将其应用于机器学习和人工智能。

A new generation of stochastic gradient decent algorithms can be efficient in finding global minimizers of possibly complicated, high-dimensional landscapes under suitable regularity assumptions for the gradient. The convergence analysis of such algorithms is linked to the study of ergodic properties for a particular class of stochastic differential equations (SDEs), so-called Langevin SDEs. The main focus of this project is the study of this class of SDEs and the nonasymptotic convergence analysis of the resulting algorithms with applications in machine learning and AI.