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.