Decentralized Personalized Federated Learning: Lower Bounds and Optimal Algorithm for All Personalization Modes

TL;DR

This paper introduces a new decentralized personalized federated learning framework that minimizes communication costs by using a network-structure-respecting penalty, providing lower bounds and optimal algorithms with practical validation.

Contribution

It develops lower bounds and provably optimal algorithms for decentralized personalized federated learning considering network structure constraints.

Findings

Proposed a network-structure-aware penalty for decentralized learning

Established lower bounds on communication and computation costs

Demonstrated practical effectiveness through numerical experiments

Abstract

This paper considers the problem of decentralized, personalized federated learning. For centralized personalized federated learning, a penalty that measures the deviation from the local model and its average, is often added to the objective function. However, in a decentralized setting this penalty is expensive in terms of communication costs, so here, a different penalty - one that is built to respect the structure of the underlying computational network - is used instead. We present lower bounds on the communication and local computation costs for this problem formulation and we also present provably optimal methods for decentralized personalized federated learning. Numerical experiments are presented to demonstrate the practical performance of our methods.