Run Procrustes, Run! On the convergence of accelerated Procrustes Flow.
Year: 2018
Type: preprint
Abstract: In this work, we present theoretical results on the convergence of non-convex accelerated gradient descent in matrix factorization models. The technique is applied to matrix sensing problems with squared loss, for the estimation of a rank $r$ optimal solution $X^\star \in \mathbb{R}^{n \times n}$. We show that the acceleration leads to linear convergence rate, even under non-convex settings where the variable $X$ is represented as $U U^\top$ for $U \in \mathbb{R}^{n \times r}$. Our result has the same dependence on the condition number of the objective --and the optimal solution-- as that of the recent results on non-accelerated algorithms. However, acceleration is observed in practice, both in synthetic examples and in two real applications: neuronal multi-unit activities recovery from single electrode recordings, and quantum state tomography on quantum computing simulators.
Source: arXiv (Cornell University)
Language: English
Subfield: Signal Processing
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2807108039