Escaping Local Minima Provably in Non-convex Matrix Sensing: A Deterministic Framework via Simulated Lifting

Abstract

We propose a deterministic simulated-oracle-direction mechanism for escaping spurious local minima in low-rank matrix sensing without explicitly lifting the problem. The method projects escape directions from an overparametrized landscape back into the original parameter space and guarantees objective decrease from existing local minima. Numerical experiments show reliable escapes with low computational overhead.