{
  "abstract": "Stochastic Push-Pull achieves linear speedup with respect to the network size $n$ on static strongly connected digraphs, but whether this speedup persists on time-varying networks remains unclear. In this work, we construct a quadratic decentralized problem on period-two networks showing that stochastic Push-Pull may fail to attain linear speedup over time-varying digraphs. For $p$-periodic networks, we identify an effective node count $n_{\\mathrm{eff}}\\le n$ that governs the leading stochastic term. Specifically, for smooth nonconvex objectives, we establish convergence upper bounds and matching lower bounds for stochastic Push-Pull with constant stepsizes, both exhibiting the leading-order dependence $Θ(1/\\sqrt{n_{\\mathrm{eff}} T})$. When $p=1$, the identity $n_{\\mathrm{eff}}=n$ recovers the usual linear speedup for static digraphs. However, periodic networks can have $n_{\\mathrm{eff}}=o(n)$, demonstrating the loss of linear speedup under temporal variation. Numerical experiments illustrate effective-count scaling and the separation between static and periodic networks, consistent with our theoretical findings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32422",
  "author_total": 4,
  "authors": [
    {
      "name": "Feiming Wang"
    },
    {
      "name": "Yutong He"
    },
    {
      "name": "Sulaiman Alghunaim"
    },
    {
      "name": "Kun Yuan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/53jm9p90sbt0e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32422",
  "fulltext_url": null,
  "id": "53jm9p90sbt0e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32422",
  "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.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1705|Distributed Control Multi-Agent Systems"
    ]
  ],
  "openalex": "W7223656243",
  "pdf_url": "https://arxiv.org/pdf/2610.32422",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/53jm9p90sbt0e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32422",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32422"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "On the Limits of Stochastic Push-Pull over Time-Varying Digraphs",
  "title_text": "On the Limits of Stochastic Push-Pull over Time-Varying Digraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/53jm9p90sbt0e",
  "venue": "arXiv",
  "versions": []
}