{
  "abstract": "The probabilistic gradient estimator (PAGE) alternates randomly between an accurate gradient refresh and a cheap recursive correction. This third expository note on recursive variance reduction explains the algorithm and gives a self-contained convergence proof for smooth nonconvex optimization. A Lyapunov function combines objective decrease with estimation error, turning the refresh probability into an explicit contraction parameter. The resulting expected oracle complexity is $O(n+\\sqrt n\\,ε^{-2})$ for finite sums and $O(ε^{-3})$ for online problems, with the other problem parameters fixed. Initialization, refreshes, and both evaluations in each gradient difference are counted. The presentation is pedagogical and makes no claim of a new algorithm or convergence rate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01523",
  "author_total": 1,
  "authors": [
    {
      "name": "Alina Lodhi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6exp4093rrx5q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01523",
  "fulltext_url": null,
  "id": "6exp4093rrx5q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01523",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01523",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6exp4093rrx5q.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01523",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01523"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Variance Reduction Note 3: The Convergence of PAGE",
  "title_text": "Variance Reduction Note 3: The Convergence of PAGE",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/6exp4093rrx5q",
  "venue": "arXiv",
  "versions": []
}