{
  "abstract": "We investigate decentralized nonsmooth nonconvex stochastic optimization over a network of $n$ nodes, with the goal of finding an $(δ,ε)$-Goldstein stationary point. The best existing algorithm achieves $O(δ^{-1}(ε^{-3}+dε^{-1}))$ sample complexity and $\\widetilde{O}(γ^{-1/2}δ^{-1}(ε^{-3}+dε^{-1}))$ communication complexity, where $d$ is the problem dimension and $γ$ is the spectral gap of the communication matrix. However, the polynomial dependence on $d$ can be a major bottleneck in high-dimensional regimes. In this paper, we propose a novel algorithm that achieves $O(δ^{-1}ε^{-3})$ sample complexity and $\\widetilde{O}(γ^{-1/2}δ^{-1}ε^{-3})$ communication complexity. The primary technique is an elegant decentralized online-to-nonconvex conversion that reduces the original problem to a decentralized online convex optimization (D-OCO) problem. A key property of our conversion is that its consensus requirements can be inherited directly from the consensus of the underlying D-OCO decisions. In particular, this property enables us to establish an explicit connection between the dimension dependence and the consensus error, which in turn shows that the polynomial dependence on $d$ can be removed with only logarithmic additional communication.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05789",
  "author_total": 5,
  "authors": [
    {
      "name": "Yuanyu Wan"
    },
    {
      "name": "Lan Xue"
    },
    {
      "name": "Haomin Bai"
    },
    {
      "name": "Tong Wei"
    },
    {
      "name": "Mingli Song"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b5czk3dqnkyhw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05789",
  "fulltext_url": null,
  "id": "b5czk3dqnkyhw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05789",
  "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",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7220654461",
  "pdf_url": "https://arxiv.org/pdf/2610.05789",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b5czk3dqnkyhw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05789",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05789"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Dimension-Free Decentralized Nonsmooth Nonconvex Stochastic Optimization",
  "title_text": "Dimension-Free Decentralized Nonsmooth Nonconvex Stochastic Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/b5czk3dqnkyhw",
  "venue": "arXiv",
  "versions": []
}