{
  "abstract": "Kullback-Leibler (KL) regularization is widely used in offline decision-making and offers several benefits, motivating recent work on the sample complexity of offline learning with respect to KL-regularized performance metrics. Nevertheless, the exact sample complexity of KL-regularized offline learning remains largely from fully characterized. In this paper, we study this question in the setting of multi-armed bandits (MABs). We provide a sharp analysis of KL-PCB (Zhao et al., 2026), showing that it achieves a sample complexity of $\\tilde{O}(ηSAC^{π^*}/ε)$ under large regularization $η= \\tilde{O}(ε^{-1})$, and a sample complexity of $\\tildeΩ(SAC^{π^*}/ε^2)$ under small regularization $η= \\tildeΩ(ε^{-1})$, where $η$ is the regularization parameter, $S$ is the number of contexts, $A$ is the number of arms, $C^{π^*}$ policy coverage coefficient at the optimal policy $π^*$, $ε$ is the desired sub-optimality, and $\\tilde{O}$ and $\\tildeΩ$ hide all poly-logarithmic factors. We further provide a pair of sharper sample complexity lower bounds, which matches the upper bounds over the entire range of regularization strengths. Overall, our results provide a nearly complete characterization of offline multi-armed bandits with KL regularization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.02141",
  "author_total": 5,
  "authors": [
    {
      "name": "Kaixuan Ji"
    },
    {
      "name": "Qiwei Di"
    },
    {
      "name": "Heyang Zhao"
    },
    {
      "name": "Qingyue Zhao"
    },
    {
      "name": "Quanquan Gu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3x3kckf816kvq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.02141",
  "fulltext_url": null,
  "id": "3x3kckf816kvq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.02141",
  "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.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7160313503",
  "pdf_url": "https://arxiv.org/pdf/2605.02141",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3x3kckf816kvq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2605.02141",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.02141"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "On the Optimal Sample Complexity of Offline Multi-Armed Bandits with KL Regularization",
  "title_text": "On the Optimal Sample Complexity of Offline Multi-Armed Bandits with KL Regularization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:59Z",
  "url": "https://research.draconitic.com/paper/3x3kckf816kvq",
  "venue": "arXiv",
  "versions": []
}