计算与应用数学拔尖博士生系列论坛——Run and Inspect Method for Nonconvex Optimization and Global Optimality Guarantees
主 题: 计算与应用数学拔尖博士生系列论坛——Run and Inspect Method for Nonconvex Optimization and Global Optimality Guarantees
报告人: Yifan Chen (Tsinghua University)
时 间: 2018-03-30 12:00-13:30
地 点: Room 1418, Sciences Building No.1
12:00-12:30 lunch；12:30-13:30 Talk
Abstract: Nonconvex optimization is ubiquitous in statistical learning and inverse problems. Many algorithms can only find stationary points. In this talk, we first introduce the Run-and-Inspect Method, which adds an “inspect” phase to existing algorithms that helps escape from non-global stationary points. Our method guarantees to locate an approximate R-local minimizer, which is optimal in its R-radius ball. Geometrically, we prove an R-local minimizer is globally optimal, up to a specific error depending on R, if the objective function can be implicitly decomposed into a smooth convex function plus a restricted function that is possibly nonconvex, nonsmooth. This also reveals the importance of studying the structure of loss functions. In the end, we will simply discuss the nice geometric structures of Wasserstein metric and its promising natural gradient flow in optimization.