{
  "abstract": "Decentralized optimization on the Stiefel manifold has broad applications in machine learning and signal processing. We propose PLADOS, a parameter-free landing algorithm for decentralized optimization on the Stiefel manifold. Each iteration combines local stochastic gradient updates with a single retraction-free communication step over the communication graph. A key convex-like property of the intersection of the nonconvex Stiefel manifold and consensus constraints is characterized through a restricted secant inequality for the penalty-only scheme, ensuring local contraction of the manifold consensus error without introducing additional parameters that require tuning. For $n$ nodes using independent local batches of size $b$, we prove that PLADOS achieves linear speedup with respect to the number of nodes with an asymptotic convergence rate of $O(σ/\\sqrt{nbK}+(nξ^2)^{1/3}/K^{2/3})$ after $K$ iterations, where $σ^2>0$ is the sampling variance and $ξ^2$ quantifies gradient heterogeneity. Experiments demonstrate stability across tested stepsizes and networks, time efficiency, and linear speedup with respect to the number of nodes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07750",
  "author_total": 2,
  "authors": [
    {
      "name": "Shu Li"
    },
    {
      "name": "Jiang Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7vc1r48axane7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07750",
  "fulltext_url": null,
  "id": "7vc1r48axane7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07750",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "1705|Distributed Control Multi-Agent Systems"
    ]
  ],
  "openalex": "W7220999977",
  "pdf_url": "https://arxiv.org/pdf/2610.07750",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7vc1r48axane7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07750",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07750"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "PLADOS: A Parameter-free Landing Algorithm for Decentralized Optimization on the Stiefel Manifold",
  "title_text": "PLADOS: A Parameter-free Landing Algorithm for Decentralized Optimization on the Stiefel Manifold",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/7vc1r48axane7",
  "venue": "arXiv",
  "versions": []
}