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

arXiv: https://arxiv.org/abs/2503.12733 · HTML: https://mlsanity.com/paper/2503.12733/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 55 references that are in the map.
- First posted on arXiv 17 Mar 2025.

## Builds on (most cited first, 17 of 17)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Self-Attentive Sequential Recommendation](https://mlsanity.com/paper/1808.09781/) (2018)
- [Secure Federated Matrix Factorization](https://mlsanity.com/paper/1906.05108/) (2019)
- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [Federated Learning via Inexact ADMM](https://mlsanity.com/paper/2204.10607/) (2022)
- [DP-ADMM: ADMM-based Distributed Learning with Differential Privacy](https://mlsanity.com/paper/1808.10101/) (2018)
- [MetaFed: Federated Learning among Federations with Cyclic Knowledge Distillation for Personalized Healthcare](https://mlsanity.com/paper/2206.08516/) (2022)
- [The proximal alternating direction method of multipliers in the nonconvex setting: convergence analysis and rates](https://mlsanity.com/paper/1801.01994/) (2018)
- [An Inertial Block Majorization Minimization Framework for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2010.12133/) (2020)
- [Share Your Representation Only: Guaranteed Improvement of the Privacy-Utility Tradeoff in Federated Learning](https://mlsanity.com/paper/2309.05505/) (2023)
- [Privacy Preserving Point-of-interest Recommendation Using Decentralized Matrix Factorization](https://mlsanity.com/paper/2003.05610/) (2020)
- [Private Alternating Least Squares: Practical Private Matrix Completion with Tighter Rates](https://mlsanity.com/paper/2107.09802/) (2021)
- [Factorbird - a Parameter Server Approach to Distributed Matrix Factorization](https://mlsanity.com/paper/1411.0602/) (2014)
- [A Framework of Inertial Alternating Direction Method of Multipliers for Non-Convex Non-Smooth Optimization](https://mlsanity.com/paper/2102.05433/) (2021)
- [Privacy-Preserving Distributed Nonnegative Matrix Factorization](https://mlsanity.com/paper/2403.18326/) (2024)
- [Fast Low-Rank Matrix Learning with Nonconvex Regularization](https://mlsanity.com/paper/1512.00984/) (2015)

## Abstract (arXiv)

Matrix completion is fundamental for predicting missing data with a wide range of applications in personalized healthcare, e-commerce, recommendation systems, and social network analysis. Traditional matrix completion approaches typically assume centralized data storage, which raises challenges in terms of computational efficiency, scalability, and user privacy. In this paper, we address the problem of federated matrix completion, focusing on scenarios where user-specific data is distributed across multiple clients, and privacy constraints are uncompromising. Federated learning provides a promising framework to address these challenges by enabling collaborative learning across distributed datasets without sharing raw data. We propose textttFedMC-ADMM for solving federated matrix completion problems, a novel algorithmic framework that combines the Alternating Direction Method of Multipliers with a randomized block-coordinate strategy and alternating proximal gradient steps. Unlike existing federated approaches, textttFedMC-ADMM effectively handles multi-block nonconvex and nonsmooth optimization problems, allowing efficient computation while preserving user privacy. We analyze the theoretical properties of our algorithm, demonstrating subsequential convergence and establishing a convergence rate of O(K-1/2), leading to a communication complexity of O(ε-2) for reaching an ε-stationary point. This work is the first to establish these theoretical guarantees for federated matrix completion in the presence of multi-block variables. To validate our approach, we conduct extensive experiments on real-world datasets, including MovieLens 1M, 10M, and Netflix. The results demonstrate that textttFedMC-ADMM outperforms existing methods in terms of convergence speed and testing accuracy.