Efficient Federated Low Rank Matrix Completion

• URL: http://arxiv.org/abs/2405.06569v2
• Date: Mon, 30 Sep 2024 21:41:12 GMT
• Title: Efficient Federated Low Rank Matrix Completion
• Authors: Ahmed Ali Abbasi, Namrata Vaswani,
• Abstract summary: We develop and analyze a solution called Alternating GD and Minimization (AltGDmin) for solving the low rank matrix completion (LRMC) problem. Our theoretical guarantees imply that AltGDmin is the most communication-efficient solution in a federated setting. We show how our lemmas can be used to provide an improved sample complexity guarantee for AltMin.
• Score: 18.471262688125645
• License:
• Abstract: In this work, we develop and analyze a Gradient Descent (GD) based solution, called Alternating GD and Minimization (AltGDmin), for efficiently solving the low rank matrix completion (LRMC) in a federated setting. LRMC involves recovering an $n \times q$ rank-$r$ matrix $\Xstar$ from a subset of its entries when $r \ll \min(n,q)$. Our theoretical guarantees (iteration and sample complexity bounds) imply that AltGDmin is the most communication-efficient solution in a federated setting, is one of the fastest, and has the second best sample complexity among all iterative solutions to LRMC. In addition, we also prove two important corollaries. (a) We provide a guarantee for AltGDmin for solving the noisy LRMC problem. (b) We show how our lemmas can be used to provide an improved sample complexity guarantee for AltMin, which is the fastest centralized solution.

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