Global Optimality of Local Search for Low Rank Matrix Recovery

@inproceedings{Bhojanapalli2016GlobalOO,
  title={Global Optimality of Local Search for Low Rank Matrix Recovery},
  author={Srinadh Bhojanapalli and Behnam Neyshabur and Nathan Srebro},
  booktitle={NIPS},
  year={2016}
}
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 from random initialization. 
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