{
  "abstract": "This paper introduces Stochastic Online Scaled Gradient Methods (SOSGM), a generalization of the recently developed adaptive preconditioning framework in arXiv:2505.23081 and arXiv:2509.11007 to stochastic optimization. Under standard assumptions, we establish convergence guarantees for SOSGM using large batchsize or variance reduction. SOSGM is compatible with popular diagonal and/or low-rank preconditioners as well as heavy-ball momentum, while maintaining memory and computation cost comparable to Adam. Extensive numerical experiments demonstrate the strong empirical performance of SOSGM. Using a diagonal preconditioner, SOSGM and its variants substantially outperform existing adaptive first-order methods across a range of statistical learning tasks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11751",
  "author_total": 4,
  "authors": [
    {
      "name": "Wanyu Zhang"
    },
    {
      "name": "Wenzhi Gao"
    },
    {
      "name": "Yinyu Ye"
    },
    {
      "name": "Madeleine Udell"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/etpnj67qvddgn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11751",
  "fulltext_url": null,
  "id": "etpnj67qvddgn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11751",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7212246789",
  "pdf_url": "https://arxiv.org/pdf/2609.11751",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/etpnj67qvddgn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.11751",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11751"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Stochastic Gradient Methods with Online Scaling",
  "title_text": "Stochastic Gradient Methods with Online Scaling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/etpnj67qvddgn",
  "venue": "arXiv",
  "versions": []
}