{
  "abstract": "In this paper, we study the regret minimization problem in episodic tabular MDPs. Our algorithm achieves the first expected regret bound scaling as $\\sqrt{H^3 S A K}$ for sufficiently large $K$, where $H$ is the episode length, $K$ is the number of episodes, and $S$ and $A$ are the numbers of states and actions, respectively. Our method is the first to match the minimax lower bound \\emph{without extra polylog factors}. We introduce a variant of UCBVI which does not maintain strictly optimistic estimates, and uses MOSS-style exploration bonuses whose logarithmic terms adapt to both visit counts and estimated variances. A key challenge is controlling the propagation of errors caused by under-optimism, which we accomplish in an occupancy-weighted way, avoiding logarithmic overhead that would be incurred by uniform-over-rows concentration. Our analysis develops time-uniform and variance-aware concentration bounds that may be of independent interest. As a corollary we also develop an algorithm for $(\\varepsilon, δ)$-PAC best-policy identification, which is the first to match the $Ω\\big(H^3 SA\\log(\\frac{1}δ)\\varepsilon^{-2}\\big)$ minimax lower bound up to constants in some regimes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40165",
  "author_total": 4,
  "authors": [
    {
      "name": "Guy Zamir"
    },
    {
      "name": "Victor Boone"
    },
    {
      "name": "Matthew Zurek"
    },
    {
      "name": "Yudong Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1g1sygs24z4rg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40165",
  "fulltext_url": null,
  "id": "1g1sygs24z4rg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40165",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40165",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1g1sygs24z4rg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:41Z",
      "native_id": "2610.40165",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40165"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Closing the Log Gap: Minimax-Optimal Regret for Episodic RL",
  "title_text": "Closing the Log Gap: Minimax-Optimal Regret for Episodic RL",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:00Z",
  "url": "https://research.draconitic.com/paper/1g1sygs24z4rg",
  "venue": "arXiv",
  "versions": []
}