Robust Personalized Federated Learning with Sparse Penalization*

Federated learning (FL) is an emerging topic due to its advantage in collaborative learning with distributed data. Due to the heterogeneity in the local data-generating mechanism, it is important to consider personalization when developing federated learning methods. In this work, we propose a personalized federated learning (PFL) method to address the robust regression problem. Specifically, we aim to learn the regression weight by solving a Huber loss with the sparse fused penalty. Additionally, we designed our personalized federated learning for robust and sparse regression (PerFL-RSR) algorithm to solve the estimation problem in the federated system efficiently. Theoretically, we show that the proposed PerFL-RSR reaches a convergence rate of O(1/T), and the proposed estimator is statistically consistent. Thorough experiments and real data analysis are conducted to corroborate the theoretical results of our proposed personalized federated learning method.

联邦学习（Federated Learning）作为新兴研究方向，凭借其在分布式数据协同学习中的优势受到广泛关注。由于本地数据生成机制存在异质性，在研发联邦学习方法时纳入个性化考量至关重要。本研究提出一种个性化联邦学习（Personalized Federated Learning）方法，用于解决鲁棒回归问题。具体而言，我们通过求解带稀疏融合惩罚项的Huber损失函数来学习回归权重。此外，我们设计了面向鲁棒稀疏回归的个性化联邦学习（Personalized Federated Learning for Robust and Sparse Regression）算法，以高效求解联邦系统中的估计问题。理论层面，我们证明所提PerFL-RSR算法可达到O(1/T)阶收敛速率，且所提出的估计量具备统计相合性。我们开展了全面的实验与真实数据分析，以验证所提个性化联邦学习方法的理论结论。