{
  "abstract": "We study episodic reinforcement learning with fixed reward and transition functions, but with episode-dependent admissible action sets that are observed at the start of each episode. Performance is measured by cumulative regret against the episode-wise optimal value, $\\sum_{k=1}^K [V^{*,M^k} - V^{π^k,M^k}]$, where $M^k$ represents the action context in the $k$-th episode. We show that the MVP algorithm naturally extends to this framework and enjoys strong theoretical guarantees. In particular, we establish a minimax regret bound of $\\widetilde{O}(\\sqrt{SAH^3K\\log L})$ for adversarial contexts, where $L$ denotes the number of possible contexts. This result implies a regret bound of $\\widetilde{O}(\\sqrt{SAH^3K})$ for stochastic contexts. We further translate the stochastic regret guarantee into a sample complexity bound of $\\widetilde{O}(SAH^3/ε^2)$ for a fixed context distribution. In addition, we derive a gap-dependent regret bound of \\[ \\widetilde O\\left( \\inf_{p\\in [0,1)} \\left( \\frac{1}{Δ_{\\min}^{p}} + pKΔ_{\\min}^{p} \\right)\\log K \\cdot \\mathrm{poly}(S,A,H) \\right), \\] where $Δ_{\\min}^{p}$ is the global $p$-trimmed positive-gap floor over suboptimal $(h,s,a)$ triples. This bound can substantially improve upon the minimax rate when the relevant suboptimality gaps are large.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.15692",
  "author_total": 2,
  "authors": [
    {
      "name": "Zijun Chen"
    },
    {
      "name": "Zihan Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a62aqyhw704w0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.15692",
  "fulltext_url": null,
  "id": "a62aqyhw704w0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.15692",
  "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",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7161554539",
  "pdf_url": "https://arxiv.org/pdf/2605.15692",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a62aqyhw704w0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:58Z",
      "native_id": "2605.15692",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.15692"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Tighter Regret Bounds for Contextual Action-Set Reinforcement Learning",
  "title_text": "Tighter Regret Bounds for Contextual Action-Set Reinforcement Learning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:58Z",
  "url": "https://research.draconitic.com/paper/a62aqyhw704w0",
  "venue": "arXiv",
  "versions": []
}