Matrix Completion has No Spurious Local Minimum

  title={Matrix Completion has No Spurious Local Minimum},
  author={Rong Ge and Jason D. Lee and Tengyu Ma},
Matrix completion is a basic machine learning problem that has wide applications, especially in collaborative filtering and recommender systems. Simple non-convex optimization algorithms are popular and effective in practice. Despite recent progress in proving various non-convex algorithms converge from a good initial point, it remains unclear why random or arbitrary initialization suffices in practice. We prove that the commonly used non-convex objective function for matrix completion has no… CONTINUE READING
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