{
  "abstract": "Sparse communication in decentralized zeroth-order learning requires compatible peer-state coordinates. We characterize this one-hop condition and develop \\textsf{ZO-COSMO}, coupling two-query estimation with average-preserving masked consensus using $q$ values per active link. Global supports serve all-neighbor mixing; matching updates require agreement only within each pair. We derive a sharp contraction-per-scalar bound within the matching class and convergence guarantees for the core and sparse-momentum updates. At fixed matching, exact moment identities characterize how shared directions preserve gradient-heterogeneity cancellation and redistribute estimation error and disagreement. Mechanism experiments cover unequal curvatures, noise, and sparse momentum. Further tests span $64$ synthetic agents and eight logical Qwen LoRA workers. At matched payload budgets, Qwen2-7B QNLI gains $3.65$ accuracy points over explicit-index Rand-$k$; edge-local updates gain $3.42$ and $2.53$ points over all-neighbor mixing on eight-worker complete and ring graphs. A matched-first-step ablation gives a $3.92$-point momentum benefit. Seed-aware and same-matching controls distinguish encoding, scheduling, and query correlation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27199",
  "author_total": 4,
  "authors": [
    {
      "name": "Shengjun Zhang"
    },
    {
      "name": "Tingyi Liu"
    },
    {
      "name": "Heng Zhang"
    },
    {
      "name": "Dong Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f4kvqsfg07gjm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27199",
  "fulltext_url": null,
  "id": "f4kvqsfg07gjm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27199",
  "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",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1705|Distributed Control Multi-Agent Systems"
    ]
  ],
  "openalex": "W7214180597",
  "pdf_url": "https://arxiv.org/pdf/2609.27199",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f4kvqsfg07gjm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27199",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27199"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "ZO-COSMO: Index-Free One-Hop Mixing for Decentralized Zeroth-Order Optimization",
  "title_text": "ZO-COSMO: Index-Free One-Hop Mixing for Decentralized Zeroth-Order Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/f4kvqsfg07gjm",
  "venue": "arXiv",
  "versions": []
}