{
  "abstract": "Posterior sampling for reinforcement learning (PSRL) is one of the simplest and most effective exploration methods, but a basic question has remained open: does unmodified PSRL achieve minimax regret without structural assumptions on the prior? We answer yes. Exact vanilla PSRL is minimax optimal in leading-order Bayesian regret under arbitrary correlated priors. The difficulty is that a posterior-sampled transition model is coupled with its own continuation value. We overcome this with a common empirical transition reference that isolates the resulting value mismatch and a Bellman-based variance argument that controls it without an extra leading-order state-space factor. For finite-horizon, time-inhomogeneous tabular MDPs with unknown stochastic rewards, this yields the minimax $\\widetilde{O}(\\sqrt{SAH^3K})$ regret rate under arbitrary joint priors over rewards and transitions. The same proof principle gives the minimax $\\widetilde{O}(d\\sqrt{H^3K})$ rate for linear-mixture MDPs under arbitrary joint parameter priors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33246",
  "author_total": 2,
  "authors": [
    {
      "name": "Taewon Goo"
    },
    {
      "name": "Kihyuk Hong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6xt6mbedrsbcf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33246",
  "fulltext_url": null,
  "id": "6xt6mbedrsbcf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33246",
  "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",
      "1702|Reinforcement Learning in Robotics"
    ]
  ],
  "openalex": "W7214740068",
  "pdf_url": "https://arxiv.org/pdf/2609.33246",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6xt6mbedrsbcf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:26Z",
      "native_id": "2609.33246",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33246"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Minimax-Optimality of Posterior Sampling for Reinforcement Learning",
  "title_text": "Minimax-Optimality of Posterior Sampling for Reinforcement Learning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/6xt6mbedrsbcf",
  "venue": "arXiv",
  "versions": []
}