Global Optimality of Local Search for Low Rank Matrix Recovery

05/23/2016

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We show that there are no spurious local minima in the non-convex factorized parametrization of low-rank matrix recovery from incoherent linear measurements. With noisy measurements we show all local minima are very close to a global optimum. Together with a curvature bound at saddle points, this yields a polynomial time global convergence guarantee for stochastic gradient descent from random initialization.

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Global Optimality of Local Search for Low Rank Matrix Recovery

Sharp Restricted Isometry Property Bounds for Low-rank Matrix Recovery Problems with Corrupted Measurements

Escaping Spurious Local Minima of Low-Rank Matrix Factorization Through Convex Lifting

Over-parametrization via Lifting for Low-rank Matrix Sensing: Conversion of Spurious Solutions to Strict Saddle Points

Deep Linear Networks Dynamics: Low-Rank Biases Induced by Initialization Scale and L2 Regularization

Global Optimality in Distributed Low-rank Matrix Factorization

Non-square matrix sensing without spurious local minima via the Burer-Monteiro approach

Flat minima generalize for low-rank matrix recovery

Global Optimality of Local Search for Low Rank Matrix Recovery

Related Research

Sharp Restricted Isometry Property Bounds for Low-rank Matrix Recovery Problems with Corrupted Measurements

Escaping Spurious Local Minima of Low-Rank Matrix Factorization Through Convex Lifting

Over-parametrization via Lifting for Low-rank Matrix Sensing: Conversion of Spurious Solutions to Strict Saddle Points

Deep Linear Networks Dynamics: Low-Rank Biases Induced by Initialization Scale and L2 Regularization

Global Optimality in Distributed Low-rank Matrix Factorization

Non-square matrix sensing without spurious local minima via the Burer-Monteiro approach

Flat minima generalize for low-rank matrix recovery