Скачать или смотреть Geometry and Symmetry in (some!) Nonconvex Optimization Problems, John Wright@Columbia University

Nonconvex optimization plays an important role in wide range of areas of science and engineering — from learning feature representations for visual classification, to reconstructing images in biology, medicine and astronomy, to disentangling spikes from multiple neurons. The worst case theory for nonconvex optimization is dismal: in general, even guaranteeing a local minimum is NP hard. However, in these and other applications, very simple iterative methods often perform surprisingly well.

In this talk, I will discuss a family of nonconvex optimization problems that can be solved to global optimality using simple iterative methods, which succeed independent of initialization. This family includes certain model problems in feature learning, imaging and scientific data analysis. These problems possess a characteristic structure, in which (i) all local minima are global, and (ii) the optimization landscape does not have any flat saddle points. I will describe how these features arise naturally as a consequence of problem symmetries, and how they lead to new types of performance guarantees for efficient methods. I will motivate these problems from microscopy, astronomy and computer vision, and show applications of our results in these domains.

Includes joint work with Yuqian Zhang, Qing Qu, Ju Sun, Henry Kuo, Yenson Lau, Dar Gilboa, Abhay Pauspathy

RPI MIDO website: https://sites.google.com/view/rpimido...