Efficient Federated Low Rank Matrix Recovery via Alternating GD and Minimization: A Simple Proof

TL;DR

This paper offers a simplified proof and improved guarantees for the sample complexity of the AltGDmin algorithm in low rank matrix recovery, enhancing understanding and efficiency of federated sensing methods.

Contribution

It presents a significantly simpler proof and an improved sample complexity guarantee for the AltGDmin algorithm in low rank matrix recovery.

Findings

Simplified proof of sample complexity guarantee

Improved theoretical guarantee for AltGDmin

Enhanced understanding of federated low rank matrix recovery

Abstract

This note provides a significantly simpler and shorter proof of our sample complexity guarantee for solving the low rank column-wise sensing problem using the Alternating Gradient Descent (GD) and Minimization (AltGDmin) algorithm. AltGDmin was developed and analyzed for solving this problem in our recent work. We also provide an improved guarantee.