{
  "abstract": "We study stochastic approximation of fixed points of a non-expansive operator $T$ when the oracle samples originate from a continuing Markovian trajectory. A direct block-minibatch implementation of Halpern iteration attains an expected last-iterate residual of order $O(\\log N/N)$, but accrues a substantive complexity of $\\tilde O(ε^{-5})$ Markovian samples. We therefore introduce a variance-reduced Markovian PAGE-Halpern method whose refresh and same-state difference blocks are analyzed through the Poisson equation. In Hilbert spaces, the cocoercivity of $I-T$ results in an $O(ε^{-3})$ sample complexity. Our main result extends this construction to a general finite-dimensional Banach space. A displacement-level Halpern bound replaces the Hilbert-space potential and yields $\\tilde O(ε^{-3})$ sample complexity. We also establish a high-probability guarantee with the same leading accuracy dependence by measuring the estimator in an auxiliary smooth norm.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.15966",
  "author_total": 4,
  "authors": [
    {
      "name": "Ege C. Kaya"
    },
    {
      "name": "Arda Fazla"
    },
    {
      "name": "M. Berk Sahin"
    },
    {
      "name": "Abolfazl Hashemi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/548h2420ngdt3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.15966",
  "fulltext_url": null,
  "id": "548h2420ngdt3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.15966",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7203701687",
  "pdf_url": "https://arxiv.org/pdf/2608.15966",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/548h2420ngdt3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2608.15966",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.15966"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A Banach-Space Theory of Markovian Halpern Iteration for Non-Expansive Maps",
  "title_text": "A Banach-Space Theory of Markovian Halpern Iteration for Non-Expansive Maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/548h2420ngdt3",
  "venue": "arXiv",
  "versions": []
}