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arXiv · 2503.20117

Exact and Linear Convergence for Federated Learning under Arbitrary Client Participation is Attainable

Bicheng Ying·Zhe Li·Haibo Yang
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Abstract

This work tackles the fundamental challenges in Federated Learning (FL) posed by arbitrary client participation and data heterogeneity, prevalent characteristics in practical FL settings. It is well-established that popular FedAvg-style algorithms struggle with exact convergence and can suffer from slow convergence rates since a decaying learning rate is required to mitigate these scenarios. To address these issues, we introduce the concept of stochastic matrix and the corresponding time-varying graphs as a novel modeling tool to accurately capture the dynamics of arbitrary client participation and the local update procedure. Leveraging this approach, we offer a fresh decentralized perspective on designing FL algorithms and present FOCUS, Federated Optimization with Exact Convergence via Push-pull Strategy, a provably convergent algorithm designed to effectively overcome the previously mentioned two challenges. More specifically, we provide a rigorous proof demonstrating that FOCUS achieves exact convergence with a linear rate regardless of the arbitrary client participation, establishing it as the first work to demonstrate this significant result.

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Bicheng Ying, Zhe Li, Haibo Yang. 2025-03-25. Exact and Linear Convergence for Federated Learning under Arbitrary Client Participation is Attainable. https://arxiv.org/abs/2503.20117

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