{
  "abstract": "Random reshuffling stochastic gradient descent (RR-SGD) is widely used for finite-sum optimization in machine learning. For convex $L$-smooth components, recent work establishes convergence guarantees for an averaged iterate with component stepsizes as large as order $1/L$. However, the final iterate is a natural output in practice, and existing last-iterate guarantees in this setting require stepsizes that scale inversely with the number of components $n$. We establish an expected objective-gap bound for the last iterate of standard RR-SGD on unconstrained problems with a constant component stepsize satisfying $0<η\\lesssim 1/(L(1 + \\log(nK)))$, where $K$ is the number of epochs. By retaining the sampling bias at random comparison points, we remove the explicit $1/n$ factor from the stepsize restriction. Combined with existing small-step bounds, our result matches the corresponding averaged-iterate convergence rate up to logarithmic factors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19444",
  "author_total": 2,
  "authors": [
    {
      "name": "Zijun Chen"
    },
    {
      "name": "Zihan Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/17sjwb8v9xg6y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19444",
  "fulltext_url": null,
  "id": "17sjwb8v9xg6y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19444",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7222345969",
  "pdf_url": "https://arxiv.org/pdf/2610.19444",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/17sjwb8v9xg6y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19444",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19444"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Large-Step Last-Iterate Convergence of Random-Reshuffling Stochastic Gradient Descent",
  "title_text": "Large-Step Last-Iterate Convergence of Random-Reshuffling Stochastic Gradient Descent",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:42Z",
  "url": "https://research.draconitic.com/paper/17sjwb8v9xg6y",
  "venue": "arXiv",
  "versions": []
}