A new generation of stochastic algorithms for sampling and optimization

新一代的随机梯度下降算法可以有效地找到可能复杂的，高维景观的梯度适当的规律性假设下的全局极小值。这种算法的收敛性分析与一类特殊的随机微分方程（SDES）的遍历性研究有关，这类随机微分方程被称为Langevin SDES。该项目的主要重点是研究这类随机微分方程，并对所得算法的非渐近收敛性进行分析，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.