Convergence of Gradient Descent with Small Initialization for Unregularized Matrix Completion

Jianhao Ma, Salar Fattahi

We study the problem of symmetric matrix completion, where the goal is to reconstruct a positive semidefinite matrix ${\mathrm{X}}^{\star }\in {\mathbb{R}}^{\mathrm{d}\times \mathrm{d}}$ of rank-$r$, paramete…