Global Optimality of Local Search for Low Rank Matrix Recovery

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}.

Cite

Text

Bhojanapalli et al. "Global Optimality of Local Search for Low Rank Matrix Recovery." Neural Information Processing Systems, 2016.

Markdown

[Bhojanapalli et al. "Global Optimality of Local Search for Low Rank Matrix Recovery." Neural Information Processing Systems, 2016.](https://mlanthology.org/neurips/2016/bhojanapalli2016neurips-global/)

BibTeX

@inproceedings{bhojanapalli2016neurips-global,
  title     = {{Global Optimality of Local Search for Low Rank Matrix Recovery}},
  author    = {Bhojanapalli, Srinadh and Neyshabur, Behnam and Srebro, Nati},
  booktitle = {Neural Information Processing Systems},
  year      = {2016},
  pages     = {3873-3881},
  url       = {https://mlanthology.org/neurips/2016/bhojanapalli2016neurips-global/}
}