{
  "abstract": "Before a new policy replaces a deployed one, we often want a certificate, computed from logged episodes, that it is better. We ask how many episodes such a certificate needs when the logging policy is known but history-dependent, and the error probability must stay below $δ$ in every environment consistent with the logs. The answer is an exponent $K^\\star$: the smallest KL divergence from the logged law to a law with the same logged action probabilities under which the target does not improve. No sound certifier stops in fewer than $\\log(1/δ)/K^\\star$ expected episodes, at any $δ$, and whenever $0<K^\\star<\\infty$ a plug-in Kelly certifier attains this rate to first order as $δ\\to0$. Coverage, computed by one backward induction, decides whether certification is impossible ($K^\\star=0$), possible at a finite rate, or possible in a constant number of episodes ($K^\\star=\\infty$). By convex duality, the optimal certificate bets on the importance-weighted advantage and also places fair bets on the logged actions, so doubly robust control variates act as hedges rather than estimators. As a consequence, no choice of off-policy estimator changes $K^\\star$, a coverage ceiling explains the curse of memory, and structural assumptions can be priced in exponent units. A cushion certifier extends the approach to trees too large to enumerate. In experiments the plug-in's median stopping time is 1.13-1.43x the lower bound on memory tasks, 1.13-1.51x on Tiger ($H\\le5$) and 1.17-1.64x on random trees. The best scalar betting baselines need up to 2.65x (memory) and 4.1x (Tiger) the plug-in's episodes; only on a few shallow random trees is a doubly robust bet faster, by at most 18%.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24345",
  "author_total": 1,
  "authors": [
    {
      "name": "Rui Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6cd16fqvvxyhr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24345",
  "fulltext_url": null,
  "id": "6cd16fqvvxyhr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24345",
  "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",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Reinforcement Learning in Robotics"
    ]
  ],
  "openalex": "W7223060104",
  "pdf_url": "https://arxiv.org/pdf/2610.24345",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6cd16fqvvxyhr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:33:54Z",
      "native_id": "2610.24345",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24345"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "The Certification Exponent: Instance-Optimal Sequential Certification of Policy Improvement from History Dependent Logs",
  "title_text": "The Certification Exponent: Instance-Optimal Sequential Certification of Policy Improvement from History Dependent Logs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/6cd16fqvvxyhr",
  "venue": "arXiv",
  "versions": []
}