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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