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PreprintCC BY-NC-ND 4.0arXiv

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 (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, 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 Tavg)), where Tavg is the average number of local update steps per communication round across devices. Numerical experiments support our findings.

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Cite

BibTeXRIS
BibTeX
@misc{wong2026large,
  title = {{Large Stepsizes Federated Learning on Logistic Regression with Linearly Separable Data: The Case of Heterogeneous Devices}},
  author = {Hok Fong Wong and Hoi-To Wai and Chung-Yiu Yau},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05915},
  eprint = {2610.05915},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05915},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Large Stepsizes Federated Learning on Logistic Regression with Linearly Separable Data: The Case of Heterogeneous Devices
AU  - Hok Fong Wong
AU  - Hoi-To Wai
AU  - Chung-Yiu Yau
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.05915
UR  - https://arxiv.org/abs/2610.05915
AB  - This paper revisits the distributed learning problem for training a multinomial logistic regression model with the Federated Averaging (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, 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_avg)), where T_avg is the average number of local update steps per communication round across devices. Numerical experiments support our findings.
ER  -