Mild logarithmic overparametrization in Burer-Monteiro nonconvex optimization yields optimal sample complexity and error for phase retrieval and rank-1 matrix sensing via a new semidefinite-structure analysis of second-order critical points.
No spurious local minima in nonconvex low rank problems: A unified geometric analysis,
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Phase retrieval and matrix sensing via benign and overparametrized nonconvex optimization
Mild logarithmic overparametrization in Burer-Monteiro nonconvex optimization yields optimal sample complexity and error for phase retrieval and rank-1 matrix sensing via a new semidefinite-structure analysis of second-order critical points.