Sharp recovery and landscape guarantees for the nonconvex matrix LASSO
非凸矩阵LASSO的精确恢复与优化景观保证
Low-rank matrix recovery can be solved to statistical optimality by convex matrix optimization under the classical assumption of restricted isometry property (RIP). However, for large problems, the convex formulation is commonly replaced by a smooth rank-constrained factored nonconvex problem for which algorithmic theory typically only guarantees convergence to second-order critical points. In this paper, we develop a sharp and statistically optimal theory for second-order…