{
  "abstract": "We study distributionally robust reinforcement learning (DR-RL) in the average-reward setting under weak communication. Our main result provides finite-sample guarantees for estimating the robust optimal average reward and learning a near-optimal policy, covering both SA-rectangular and S-rectangular structures with divergence-based and distance-based uncertainty sets. Specifically, for Kullback--Leibler and $f_k$-divergence balls, we establish explicit radius conditions under which the robust average-reward Bellman equation admits a constant-gain solution, while for total variation and Wasserstein balls, any positive radius suffices without requiring the nominal MDP to be weakly communicating. Our algorithm is prior-knowledge-free and achieves sample complexities of $\\widetilde O(|\\mathcal{S}||\\mathcal{A}|p_{\\wedge}^{-1}\\operatorname{Span}^{2}(u_δ^{\\ast})ε^{-2})$ for estimating the robust optimal average reward and $\\widetilde O(|\\mathcal{S}||\\mathcal{A}|p_{\\wedge}^{-2}\\operatorname{Span}^{2}(u_δ^{\\ast})ε^{-2})$ for learning an $ε$-optimal policy. Here, $p_{\\wedge}$ is the smallest positive nominal transition probability and $u_δ^{\\ast}$ is a robust optimal bias function. We further provide an almost-tight explicit upper bound on $\\operatorname{Span}(u_δ^{\\ast})$. Finally, we validate the predicted $n^{-1/2}$ convergence rate through numerical experiments.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32727",
  "author_total": 3,
  "authors": [
    {
      "name": "Chenyu Lu"
    },
    {
      "name": "Zijun Chen"
    },
    {
      "name": "Nian Si"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d0b5cf8q4e1mp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32727",
  "fulltext_url": null,
  "id": "d0b5cf8q4e1mp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32727",
  "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",
      "math.OC"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Reinforcement Learning in Robotics"
    ]
  ],
  "openalex": "W7214717020",
  "pdf_url": "https://arxiv.org/pdf/2609.32727",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d0b5cf8q4e1mp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32727",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32727"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Distributionally Robust Average-Reward Reinforcement Learning: Finite-Sample Guarantees under Weak Communication",
  "title_text": "Distributionally Robust Average-Reward Reinforcement Learning: Finite-Sample Guarantees under Weak Communication",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/d0b5cf8q4e1mp",
  "venue": "arXiv",
  "versions": []
}