Global Optimality of Local Search for Low Rank Matrix Recovery
Machine Learning
2016-05-30 v2 Machine Learning
Optimization and Control
Abstract
We show that there are no spurious local minima in the non-convex factorized parametrization of low-rank matrix recovery from incoherent linear measurements. With noisy measurements we show all local minima are very close to a global optimum. Together with a curvature bound at saddle points, this yields a polynomial time global convergence guarantee for stochastic gradient descent {\em from random initialization}.
Keywords
Cite
@article{arxiv.1605.07221,
title = {Global Optimality of Local Search for Low Rank Matrix Recovery},
author = {Srinadh Bhojanapalli and Behnam Neyshabur and Nathan Srebro},
journal= {arXiv preprint arXiv:1605.07221},
year = {2016}
}
Comments
21 pages, 3 figures