{
  "abstract": "We study decentralized minimization of a smooth network average that is globally quasar-convex with respect to a fixed minimizer; the node functions may be nonconvex and need not share a minimizer. A unit-rate Poisson clock drives an exactly simulable continuized process: between events the state follows a closed-form accelerated flow, and each event uses one oracle vector. One master theorem covers oracles with a predictable bias and a state-dependent variance and keeps the inverse-quadratic term $\\mathcal{O}(LR_0^2/(γ^2T^2))$; one selected-row lemma supplies the oracle moments of three network implementations. CQA-Net keeps a common state, mixes local rows for finitely many rounds, and disseminates one uniformly selected row; its oracle is unbiased at every mixing depth, so incomplete averaging affects only the variance. A walking token removes dissemination, the shared clock, and the shared root, and an importance weight keeps it unbiased on fixed graphs. D-CQA keeps local states and mixes them; under bounded heterogeneity it needs $\\widetilde{\\mathcal{O}}(\\sqrtχ\\sqrt{L}R_0/(γθ\\sqrt{\\varepsilon}))$ communication rounds and no dissemination. Changing graphs enter through certified operator norms. Experiments on a certified nonconvex regression on static and changing graphs compare the three implementations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04597",
  "author_total": 5,
  "authors": [
    {
      "name": "Ilya Kuruzov"
    },
    {
      "name": "Artem Agafonov"
    },
    {
      "name": "Vadim Abronin"
    },
    {
      "name": "Darina Dvinskikh"
    },
    {
      "name": "Alexander Gasnikov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d69tpmv7w4dab.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04597",
  "fulltext_url": null,
  "id": "d69tpmv7w4dab",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04597",
  "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/2611.04597",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d69tpmv7w4dab.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04597",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04597"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Continuized Quasar-Convex Acceleration via an Unbiased Finite-Mixing Network Oracle",
  "title_text": "Continuized Quasar-Convex Acceleration via an Unbiased Finite-Mixing Network Oracle",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:38Z",
  "url": "https://research.draconitic.com/paper/d69tpmv7w4dab",
  "venue": "arXiv",
  "versions": []
}