{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05915",
  "author_total": 3,
  "authors": [
    {
      "name": "Hok Fong Wong"
    },
    {
      "name": "Hoi-To Wai"
    },
    {
      "name": "Chung-Yiu Yau"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ajt5573p8qnf3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05915",
  "fulltext_url": null,
  "id": "ajt5573p8qnf3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05915",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.05915",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ajt5573p8qnf3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05915",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05915"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Large Stepsizes Federated Learning on Logistic Regression with Linearly Separable Data: The Case of Heterogeneous Devices",
  "title_text": "Large Stepsizes Federated Learning on Logistic Regression with Linearly Separable Data: The Case of Heterogeneous Devices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/ajt5573p8qnf3",
  "venue": "arXiv",
  "versions": []
}