Personalized Federated Learning via Convex Clustering

TL;DR

This paper introduces a novel federated learning framework that automatically clusters user models through convex clustering, balancing personalization and generalization without prior knowledge of cluster structures.

Contribution

It develops a new convex clustering-based algorithm for personalized federated learning, with theoretical bounds and an efficient PDMM-based solution.

Findings

Enables automatic model clustering without prior cluster info

Balances personalization and generalization effectively

Provides theoretical bounds for parameter selection

Abstract

We propose a parametric family of algorithms for personalized federated learning with locally convex user costs. The proposed framework is based on a generalization of convex clustering in which the differences between different users' models are penalized via a sum-of-norms penalty, weighted by a penalty parameter $\lambda$. The proposed approach enables "automatic" model clustering, without prior knowledge of the hidden cluster structure, nor the number of clusters. Analytical bounds on the weight parameter, that lead to simultaneous personalization, generalization and automatic model clustering are provided. The solution to the formulated problem enables personalization, by providing different models across different clusters, and generalization, by providing models different than the per-user models computed in isolation. We then provide an efficient algorithm based on the Parallel Direction Method of Multipliers (PDMM) to solve the proposed formulation in a federated server-users setting. Numerical experiments corroborate our findings. As an interesting byproduct, our results provide several generalizations to convex clustering.