{
  "abstract": "We study first-order regret guarantees for adversarial bandits with a fixed, known directed feedback graph. For strongly observable graphs, [ACBDK15] establishes a minimax regret of $\\widetildeΘ(\\sqrt{αT})$, where $α$ denotes the independence number of the graph and $T$ denotes the horizon. On the other hand, the best existing first-order bound scales as $\\widetilde{O}(\\sqrt{(κ+1) L^\\star})$ [LLZ20], where $κ$ denotes the clique partition number, satisfying $κ+1\\geqα$, and $L^\\star$ denotes the cumulative loss of the best arm, leaving a gap between the graph dependence in worst-case and first-order guarantees. In this paper, we bridge this gap by obtaining an expected regret bound of $\\widetilde{O}(\\sqrt{αL^\\star}+α)$. Our first result is an algorithm for the special case of self-aware graphs, in which every vertex has a self-loop. The algorithm combines the update of EXP3 [ACBFS02] with a sampling rule inspired by exploration by optimization [LS20]. More specifically, we construct a map whose fixed points yield sampling distributions that control the one-round regret remainder in terms of the learner's loss and the graph's independence number, which is crucial in deriving optimal first-order guarantees. We further show that a sufficiently accurate fixed point can be computed in polynomial time by a geometrically convergent iteration. Finally, we extend the algorithm to general strongly observable graphs and achieve the same $\\widetilde{O}(\\sqrt{αL^\\star}+α)$ guarantee by adapting the two-level aggregation approach of [LLZ20].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40861",
  "author_total": 4,
  "authors": [
    {
      "name": "Mengxiao Zhang"
    },
    {
      "name": "Yuheng Zhang"
    },
    {
      "name": "Haipeng Luo"
    },
    {
      "name": "Paul Mineiro"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7t0c8d819aj55.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40861",
  "fulltext_url": null,
  "id": "7t0c8d819aj55",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40861",
  "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/2610.40861",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7t0c8d819aj55.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:25Z",
      "native_id": "2610.40861",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40861"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Near-Optimal First-Order Regret for Bandits with Feedback Graphs",
  "title_text": "Near-Optimal First-Order Regret for Bandits with Feedback Graphs",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/7t0c8d819aj55",
  "venue": "arXiv",
  "versions": []
}