{
  "abstract": "This paper investigates the distributed online bilevel optimization problem with time-varying inequality constraints. In this setting, a multi-agent network is confronted with a hierarchical decision-making task characterized by coupling between the inner and outer optimization levels. We first propose a communication-efficient single-loop distributed online primal--dual algorithm based on communication compression, which tracks both the inner-level solution and the Hessian-inverse-vector product using only one update per-round. We show that this algorithm achieves a dynamic network regret bound of $\\mathcal{O}(T^{\\max\\{θ_1,1-θ_1\\}}+T^{θ_1 } P_T+H_{1,T}+E_{1,T})$, where~$θ_1 \\in (0,1)$, $P_T$ is the outer-level path variation, $H_{1,T}$ is the inner-level path variation, and $E_{1,T}$ is the gradient path variation alongside a network cumulative constraint violation bound of $\\mathcal{O}(T^{1-θ_1/2})$, which is further reduced to $\\mathcal{O}(T^{1-θ_1})$ under Slater's condition. Furthermore, to eliminate the dependence of regret on the inner-level and gradient path variation, we propose a novel adaptive multi-loop distributed online algorithm to control the inner-level approximation accuracy at each round. By dynamically adjusting the number of inner-level updates based on a gradient-norm tolerance condition, this algorithm yields an improved dynamic network regret bound of $\\mathcal{O}(T^{\\max\\{θ_1,1-θ_1\\}}+T^{θ_1 } P_T)$ which depends solely on the outer-level path variation while maintaining the same network cumulative constraint violation bound. Finally, numerical simulations verify the effectiveness of the proposed algorithms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26911",
  "author_total": 5,
  "authors": [
    {
      "name": "Fan Li"
    },
    {
      "name": "Xinlei Yi"
    },
    {
      "name": "Guanghui Wen"
    },
    {
      "name": "Yang Shi"
    },
    {
      "name": "Tao Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fff0v5bxq8td2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26911",
  "fulltext_url": null,
  "id": "fff0v5bxq8td2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26911",
  "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": "W7223107344",
  "pdf_url": "https://arxiv.org/pdf/2610.26911",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fff0v5bxq8td2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.26911",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26911"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Dynamic Regret and Tightened Constraint Violation for Communication-Efficient Distributed Online Bilevel Optimization",
  "title_text": "Dynamic Regret and Tightened Constraint Violation for Communication-Efficient Distributed Online Bilevel Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/fff0v5bxq8td2",
  "venue": "arXiv",
  "versions": []
}