{
  "abstract": "We study model-free online reinforcement learning (RL) for episodic tabular Markov decision processes, focusing on both gap-dependent regret and policy switching cost. While fine-grained gap-dependent analysis has been established for model-free RL algorithms using Hoeffding-type exploration bonuses, such results for model-free algorithms with variance-based exploration bonuses remain unknown, despite their superior worst-case and coarse-grained gap-dependent guarantees. In this paper, we resolve this open problem by establishing the first fine-grained gap-dependent regret upper bound for UCB-Bernstein+, a refined UCB-Bernstein algorithm, in variance-aware model-free online RL. Moreover, by integrating a stage-wise policy update design into our fine-grained framework and using refined variance-based bonuses, we achieve the best-known gap-dependent local switching cost to date. In addition, our analysis yields improved worst-case guarantees for both regret and local switching cost over the original UCB-Bernstein algorithm. Numerical experiments further demonstrate that UCB-Bernstein+ achieves favorable empirical performance in both regret and local switching cost.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04752",
  "author_total": 3,
  "authors": [
    {
      "name": "Haochen Zhang"
    },
    {
      "name": "Lingzhou Xue"
    },
    {
      "name": "Zhong Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3z6790zn6mx8p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04752",
  "fulltext_url": null,
  "id": "3z6790zn6mx8p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04752",
  "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.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7220683973",
  "pdf_url": "https://arxiv.org/pdf/2610.04752",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3z6790zn6mx8p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:16Z",
      "native_id": "2610.04752",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04752"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Variance-Aware Fine-Grained Gap-Dependent Bounds for Online Reinforcement Learning",
  "title_text": "Variance-Aware Fine-Grained Gap-Dependent Bounds for Online Reinforcement Learning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:16Z",
  "url": "https://research.draconitic.com/paper/3z6790zn6mx8p",
  "venue": "arXiv",
  "versions": []
}