{
  "abstract": "We study decentralized composite finite-sum optimization over a fixed connected undirected network, where agents access local component functions through function evaluations and share a possibly nonsmooth convex regularizer. In this setting, standard two-point gradient estimators can retain nonvanishing variance at a solution, complicating their integration with gradient tracking. We propose Distributed Zeroth-Order Incremental Variance Reduction (Distributed ZIVR), which combines incrementally updated component-gradient estimates with a proximal gradient-tracking scheme. The method admits an implementation using a constant number of function evaluations per agent at every iteration, without intermittent full-component or full-coordinate refreshes. For convex smooth component functions and strongly convex local averages, we establish linear convergence up to a controllable finite-difference error. With the finite-difference radius chosen for the target accuracy, Chebyshev-accelerated mixing yields a per-agent oracle complexity of $\\widetilde{O}(d(m+κ)\\log(1/ε))$ for expected squared solution error $ε$, where $d$ is the dimension, $m$ is the number of components per agent, and $κ$ is the condition number. This matches the centralized ZIVR oracle bound, while the communication bound has only an inverse square-root dependence on the network spectral gap. Experiments on logistic and robust regression demonstrate rapid reduction of solution and consensus errors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41615",
  "author_total": 2,
  "authors": [
    {
      "name": "Silan Zhang"
    },
    {
      "name": "Yujie Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cdsz3jbn5mamx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41615",
  "fulltext_url": null,
  "id": "cdsz3jbn5mamx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41615",
  "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.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41615",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cdsz3jbn5mamx.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41615",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41615"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Distributed Zeroth-Order Composite Finite-Sum Optimization via Incremental Variance Reduction",
  "title_text": "Distributed Zeroth-Order Composite Finite-Sum Optimization via Incremental Variance Reduction",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/cdsz3jbn5mamx",
  "venue": "arXiv",
  "versions": []
}