{
  "abstract": "Reinforcement learning (RL) embodies a foundational paradigm for sequential decision-making in the face of uncertainty. The rapid growth of model complexity in emerging applications has significantly amplified the challenges of achieving data-efficient RL, particularly in sample-starved scenarios where data collection may be costly, time-consuming, or even high-stakes. Consequently, understanding and improving the data efficiency of RL algorithms has become a central problem of both fundamental theoretical interest and practical importance. Despite decades of research, the statistical underpinnings of RL remained remarkably underdeveloped until relatively recently, particularly in the finite-sample regimes most relevant to modern practice. Over the past few years, there has been a surge of activity advancing the frontiers of non-asymptotic statistical RL theory, drawing on ideas from high-dimensional statistics and probability, information theory, and statistical learning theory. In this monograph, we present a non-asymptotic treatment for RL based on tabular Markov decision processes, focusing on three canonical sampling mechanisms --- RL with a generative model, online RL, and offline RL --- together with two algorithmic paradigms: model-based and model-free approaches. Centered around non-asymptotic sample complexity analysis, our treatment emphasizes minimax-optimal algorithm design, particularly methods that attain statistical optimality without significant burn-in costs, as well as sharp statistical characterizations of several widely used RL algorithms. Whenever possible, we provide largely self-contained analyses together with intuitive explanations. We also briefly discuss several extensions, such as robust RL, competitive multi-agent RL, federated RL, uncertainty quantification, and RL from human feedback.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41903",
  "author_total": 6,
  "authors": [
    {
      "name": "Yuxin Chen"
    },
    {
      "name": "Yuejie Chi"
    },
    {
      "name": "Jianqing Fan"
    },
    {
      "name": "Gen Li"
    },
    {
      "name": "Yuting Wei"
    },
    {
      "name": "Yuling Yan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8yebfqtz5m7y9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41903",
  "fulltext_url": null,
  "id": "8yebfqtz5m7y9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41903",
  "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.IT"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41903",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8yebfqtz5m7y9.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41903",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41903"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Statistical Foundations of Reinforcement Learning: A Non-Asymptotic Perspective",
  "title_text": "Statistical Foundations of Reinforcement Learning: A Non-Asymptotic Perspective",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/8yebfqtz5m7y9",
  "venue": "arXiv",
  "versions": []
}