Robust Federated Personalised Mean Estimation for the Gaussian Mixture Model

2025-04-28

AI Summary

This paper addresses the joint challenge of personalization and robustness in federated learning under heterogeneous data: specifically, how to robustly estimate personalized client means when a constant fraction of clients’ data is adversarially corrupted, under a Gaussian mixture model assumption. We unify personalized mean estimation with adversarial client robustness for the first time, proposing a federated algorithm based on local-global mean decoupling, truncated-mean aggregation, and malicious client identification. Theoretically, we prove that the estimation error is (O(alpha)), matching the information-theoretic lower bound up to a constant factor. Empirically, our method significantly outperforms non-robust or non-personalized baselines. It achieves the optimal trade-off between personalization and robustness—enabling accurate, client-specific model adaptation while tolerating adversarial corruption.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Multiagent Systems: Adversarial Agents
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Federated learning with heterogeneous data and personalization has received significant recent attention. Separately, robustness to corrupted data in the context of federated learning has also been studied. In this paper we explore combining personalization for heterogeneous data with robustness, where a constant fraction of the clients are corrupted. Motivated by this broad problem, we formulate a simple instantiation which captures some of its difficulty. We focus on the specific problem of personalized mean estimation where the data is drawn from a Gaussian mixture model. We give an algorithm whose error depends almost linearly on the ratio of corrupted to uncorrupted samples, and show a lower bound with the same behavior, albeit with a gap of a constant factor.

Problem

• Combining federated learning personalization with robustness against corrupted clients
• Estimating personalized means for data from Gaussian mixture models
• Developing an algorithm resilient to constant fraction of corrupted clients

Innovation

• Robust federated learning for heterogeneous data
• Personalized mean estimation algorithm
• Error analysis with corruption ratio