{
  "abstract": "\\emph{Kullback-Leibler} (KL) regularization is ubiquitous in reinforcement learning algorithms in the form of \\emph{reverse} or \\emph{forward} KL. Recent studies have demonstrated $ε^{-1}$-type fast rates for decision making under reverse KL regularization, in contrast to the standard $ε^{-2}$-type sample complexity. However, for forward-KL-regularized objectives, existing statistical analyses are either not applicable or result in $\\tilde{O}(ε^{-2})$ slow rates. We take the first step towards addressing this problem via a streamlined analysis of forward-KL-regularized offline CBs. We give the first $\\tilde{O}(ε^{-1})$ upper bounds in tabular and general function approximation settings, both under notions of \\emph{single-policy concentrability}. In particular, our convex-analytical pipeline unifies these settings by exploiting the pessimism principle in a novel way and completely bypasses the proof routines in previous works based on the mean value theorem, which might be of independent interest. Moreover, we provide rate-optimal lower bounds, manifesting the tightness of our upper bounds in terms of statistical rates. Our lower bounds also demonstrate that the forward-KL-regularized sample complexity recovers the unregularized slow rate in the low-regularization regime, similarly to the reverse-KL regularization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.09214",
  "author_total": 4,
  "authors": [
    {
      "name": "Qingyue Zhao"
    },
    {
      "name": "Kaixuan Ji"
    },
    {
      "name": "Heyang Zhao"
    },
    {
      "name": "Quanquan Gu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bjb739dabkqhg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.09214",
  "fulltext_url": null,
  "id": "bjb739dabkqhg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.09214",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.AI"
    ],
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7160893033",
  "pdf_url": "https://arxiv.org/pdf/2605.09214",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bjb739dabkqhg.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2605.09214",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.09214"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability",
  "title_text": "Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:50Z",
  "url": "https://research.draconitic.com/paper/bjb739dabkqhg",
  "venue": "arXiv",
  "versions": []
}