Large Stepsizes Federated Learning on Logistic Regression with Linearly Separable Data: The Case of Heterogeneous Devices

Hok Fong Wong; Hoi-To Wai; Chung-Yiu Yau

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arXiv · 2610.05915

Large Stepsizes Federated Learning on Logistic Regression with Linearly Separable Data: The Case of Heterogeneous Devices

Hok Fong Wong·Hoi-To Wai·Chung-Yiu Yau

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Abstract

This paper revisits the distributed learning problem for training a multinomial logistic regression model with the Federated Averaging ($\texttt{FedAvg}$) algorithm. We concentrate on a scenario with arbitrarily large stepsizes and heterogeneous update rules where the devices may perform a different number of local updates in each round. We show that, with linearly separable data, $\texttt{FedAvg}$ is stable with any stepsizes and the objective values converge to zero at the rate of ${\cal O}(1/R)$, where $R$ is the number of communication rounds. Our result also demonstrates that the effects of device heterogeneity vanish asymptotically. For sufficiently large $R$, the objective values decrease monotonically and is bounded by ${\cal O}( 1 / (R T_{\rm avg}))$, where $T_{\rm avg}$ is the average number of local update steps per communication round across devices. Numerical experiments support our findings.

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BibTeX RIS

Hok Fong Wong, Hoi-To Wai, Chung-Yiu Yau. 2026-10-05. Large Stepsizes Federated Learning on Logistic Regression with Linearly Separable Data: The Case of Heterogeneous Devices. https://arxiv.org/abs/2610.05915

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