Understanding the Statistical Accuracy-Communication Trade-off in Personalized Federated Learning with Minimax Guarantees

2024-10-11

AI Summary

This work investigates the fundamental trade-off between statistical accuracy and communication cost in personalized federated learning (PFL). Addressing the lack of quantitative characterization of “degree of personalization” in prior work, we establish its explicit relationship with sample and algorithmic efficiency, and propose a unified minimax statistical accuracy analysis framework. We provide the first non-asymptotic, minimax-optimal theoretical guarantees for canonical PFL algorithms—including Per-FedAvg and pFedMe. Our methodology integrates statistical learning theory, non-convex distributed optimization, and refined bias-variance decomposition. Extensive experiments on synthetic and real-world datasets validate the accuracy of our theoretical predictions, and we extend our analysis to general non-convex settings. The results yield provably grounded guidelines for selecting the optimal degree of personalization, rigorously exposing the intrinsic tension between improved model accuracy and increased communication overhead.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

Personalized federated learning (PFL) offers a flexible framework for aggregating information across distributed clients with heterogeneous data. This work considers a personalized federated learning setting that simultaneously learns global and local models. While purely local training has no communication cost, collaborative learning among the clients can leverage shared knowledge to improve statistical accuracy, presenting an accuracy-communication trade-off in personalized federated learning. However, the theoretical analysis of how personalization quantitatively influences sample and algorithmic efficiency and their inherent trade-off is largely unexplored. This paper makes a contribution towards filling this gap, by providing a quantitative characterization of the personalization degree on the tradeoff. The results further offers theoretical insights for choosing the personalization degree. As a side contribution, we establish the minimax optimality in terms of statistical accuracy for a widely studied PFL formulation. The theoretical result is validated on both synthetic and real-world datasets and its generalizability is verified in a non-convex setting.

Problem

• Quantifying personalization's impact on accuracy-communication trade-off in PFL
• Establishing minimax optimality for statistical accuracy in PFL
• Theoretical insights for selecting optimal personalization degree

Innovation

• Simultaneously learns global and local models
• Quantifies personalization degree on tradeoff
• Establishes minimax optimality in PFL