Davood Hajinezhad from Dr. Hong’s research group will be giving the talk tomorrow. The title is “Nonconvex Low Rank Matrix Factorization via Inexact First Order Oracle”. The details are as follows:
Date: March 31st, Friday
Time: 3:00 – 4:00 pm
Venue: 2222 Coover hall
Davood’s abstract: We study the low rank matrix factorization problem via nonconvex optimization. Compared with the convex relaxation approach, nonconvex optimization exhibits superior empirical performance for large scale low rank matrix estimation. However, the understanding of its theoretical guarantees is limited. To bridge this gap, we exploit the notion of inexact first order oracle, which naturally appears in low rank matrix factorization problems such as matrix sensing and completion. Particularly, our analysis shows that a broad class of nonconvex optimization algorithms, including alternating minimization and gradient-type methods, can be treated as solving two sequences of convex optimization algorithms using inexact first order oracle. Thus we can show that these algorithms converge geometrically to the global optima and recover the true low rank matrices under suitable conditions. Numerical results are provided to support our theory.