{
  "abstract": "We study online learning with directed weakly observable feedback graphs and propose a Follow-the-Perturbed-Leader (FTPL) policy that achieves best-of-both-worlds guarantee with nearly linear expected time complexity. To preserve the simple structure of FTPL, we develop a novel graph-based loss estimator that combines forced exploration, conditional geometric resampling and adaptive learning rates with surrogate probabilities. Our policy achieves $\\tilde{\\mathcal{O}}(δ_*^{1/3} T^{2/3})$ regret for adversarial regimes as well as $\\tilde{\\mathcal{O}}(δ_* \\log T / Δ_{\\min}^2)$ regret for stochastic regimes, where $δ_*$ and $Δ$, respectively, denote the fractional weak domination number and the suboptimality gap. These results show that refined guarantees for problems with minimax regret of $Θ(T^{2/3})$ can be obtained through appropriately designed adaptive learning rates and loss estimators without sacrificing the simplicity of FTPL.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04307",
  "author_total": 2,
  "authors": [
    {
      "name": "Jongyeong Lee"
    },
    {
      "name": "Hyundam Yoo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1z86tshtzz71f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04307",
  "fulltext_url": null,
  "id": "1z86tshtzz71f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04307",
  "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",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04307",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1z86tshtzz71f.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:34Z",
      "native_id": "2611.04307",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04307"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Nearly Linear-Time Follow-the-Perturbed-Leader for Weakly Observable Graph Bandits",
  "title_text": "Nearly Linear-Time Follow-the-Perturbed-Leader for Weakly Observable Graph Bandits",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:10Z",
  "url": "https://research.draconitic.com/paper/1z86tshtzz71f",
  "venue": "arXiv",
  "versions": []
}