A Linearized Alternating Direction Multiplier Method for Federated Matrix Completion Problems.

Area of Science:

• Computer Science
• Machine Learning
• Data Science

Background:

• Matrix completion (MC) is crucial for predicting missing data across various fields.
• Traditional MC methods face challenges with centralized data storage, including privacy, scalability, and efficiency.
• Federated learning (FL) offers a solution for collaborative learning on distributed datasets without raw data sharing.

Purpose of the Study:

• To address the challenges of federated matrix completion (MC) in privacy-sensitive applications.
• To propose a novel algorithmic framework, FedMC-ADMM, for solving federated MC problems.
• To provide theoretical guarantees for federated MC with multiblock variables.

Main Methods:

• Developed FedMC-ADMM, combining alternating direction method of multipliers (ADMM) with randomized block-coordinate and proximal gradient strategies.
• Designed to handle multiblock nonconvex and nonsmooth optimization problems inherent in federated MC.
• Analyzed theoretical convergence properties, establishing subsequential convergence and a convergence rate of O(K^{-1/2}).

Main Results:

• FedMC-ADMM demonstrates subsequential convergence with a communication complexity of O(epsilon^{-2}).
• The algorithm effectively handles multiblock nonconvex and nonsmooth optimization problems.
• Extensive experiments on MovieLens and Netflix datasets show FedMC-ADMM surpasses existing methods in convergence speed and accuracy.

Conclusions:

• FedMC-ADMM offers an efficient and private solution for federated matrix completion.
• This work provides the first theoretical guarantees for federated MC with multiblock variables.
• The proposed method shows significant improvements in performance for real-world applications.