Global Optimality of Local Search for Low Rank Matrix Recovery
  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}. 
Srinadh Bhojanapalli, Behnam Neyshabur, Nathan Srebro
stat.ML cs.LG math.OC