{
  "abstract": "Standard reinforcement learning (RL) algorithms based on Markov Decision Processes (MDPs) are vulnerable to sim-to-real gaps. To address this issue, distributionally robust RL algorithms based on robust MDPs (RMDPs) have been proposed, for ensuring that agents can perform reliably to unpredictable conditions in real-world environments. Despite of the rich literature, \\revision{an efficient model-free method is still lacking} for robust RL, particularly for Markovian data, which is more relevant in practical applications. In this work, we take a step towards settling this problem by proposing a sample efficient (asynchronous Q-learning) algorithm for robust RL. In particular, consider a $γ$-discounted infinite-horizon RMDP with state space $\\mathcal{S}$ and action space $\\mathcal{A}$, where the uncertainty set is specified by the total variation (TV) distance with uncertainty level $σ$. Assuming access to a single trajectory of Markovian samples induced by a behavior policy and the nominal transition kernel, the sample complexity of the proposed Q-learning algorithm --- to achieve an entrywise $\\varepsilon$-approximation of the optimal Q-function --- is bounded by $$ \\frac{1}{μ_{\\mathsf{min}}\\varepsilon^2(1-γ)^3\\max\\{1-γ,σ\\}} + \\frac{t_{\\mathsf{mix}}}{μ_{\\mathsf{min}}(1-γ)} $$ up to logarithmic factors. Here, $t_{\\mathsf{mix}}$ and $μ_{\\mathsf{min}}$ denote the mixing time and the minimum state-action occupancy probability of the sample trajectory, respectively. This result is nearly minimax optimal, with an additional factor of $\\frac{1}{1-γ}$. Moreover, it achieves a significant improvement over existing bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35656",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuchen Jiao"
    },
    {
      "name": "Gen Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/61gaskdcrpw9s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35656",
  "fulltext_url": null,
  "id": "61gaskdcrpw9s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35656",
  "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.LG"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1702|Reinforcement Learning in Robotics"
    ]
  ],
  "openalex": "W7223887523",
  "pdf_url": "https://arxiv.org/pdf/2610.35656",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/61gaskdcrpw9s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35656",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35656"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Provably Efficient Q-learning for Robust Reinforcement Learning",
  "title_text": "Provably Efficient Q-learning for Robust Reinforcement Learning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:49Z",
  "url": "https://research.draconitic.com/paper/61gaskdcrpw9s",
  "venue": "arXiv",
  "versions": []
}