{
  "abstract": "We present an oracle-optimal method for finite-sum monotone inclusions under mean-square Lipschitz continuity. Our switching regularization method finds a point $y$ and a certificate $g\\in G(y)$ with $(\\mathbb{E}\\|F(y)+g\\|^2)^{1/2}\\le\\varepsilon$ using $\\mathcal{O}(n+\\sqrt{n}LR/\\varepsilon)$ expected component evaluations and resolvent evaluations. It removes the additive $n\\log n$ cost of restarting a variance-reduced solver at every regularization stage by switching to a centered stochastic proximal iteration at regularization strength $L/\\sqrt{n}$. Carrying an operator estimate between the remaining stages limits their total cost to $\\mathcal{O}(n)$. A matching $Ω(n+\\sqrt{n}LR/\\varepsilon)$ lower bound holds for randomized linear-span component-oracle algorithms with adaptive stopping and expected query budgets. Thus, for $0<\\varepsilon\\le LR/2$, our method attains the optimal worst-case expected component complexity in this oracle model, up to universal constants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05038",
  "author_total": 1,
  "authors": [
    {
      "name": "Qihao Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/01zajjpd6fr3d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05038",
  "fulltext_url": null,
  "id": "01zajjpd6fr3d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05038",
  "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",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7220685081",
  "pdf_url": "https://arxiv.org/pdf/2610.05038",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/01zajjpd6fr3d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05038",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05038"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Optimal Oracle Complexity for Finite-Sum Monotone Inclusions",
  "title_text": "Optimal Oracle Complexity for Finite-Sum Monotone Inclusions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/01zajjpd6fr3d",
  "venue": "arXiv",
  "versions": []
}