Rank Overparameterization and Global Optimality Certification in Low-Rank Matrix Estimation

Explore the intricacies of nonconvex optimization over low-rank matrices in this 52-minute lecture from the USC Probability and Statistics Seminar. Delve into the challenges of achieving global optimality in large-scale problems and the practical implications for critical applications like electricity grid operations. Examine how rank overparameterization can mitigate nonconvexity issues, making spurious local minima increasingly rare as rank increases. Discover a novel approach to certifying global optimality convergence using rank deficiency, and learn about an efficient preconditioner that restores linear convergence rates in overparameterized cases. Gain insights from related research papers on rank overparameterization and global optimality certification, presented by Richard Y. Zhang from the University of Illinois Urbana-Champaign.