{
  "abstract": "Many generative systems return multiple candidate responses and are evaluated according to the best one. Recent work shows that, when demonstrations are optimal, pass@$k$ can reduce the sample complexity of learning from demonstrations by a logarithmic factor in $k$. We ask what happens when the demonstrator is not assumed to be optimal. We find that multiple responses provide a qualitatively stronger benefit in this setting. In a finite reward-class model with no reward feedback, moving from pass@$1$ to any pass@$k$ with $k\\ge2$ changes the worst-case dependence on target accuracy from $1/\\varepsilon^2$ to $1/\\varepsilon$, uniformly over demonstrator quality. Under standard evaluation, where an unknown reward is fixed before training, increasing $k$ provides an additional and distinct benefit: the optimal dependence on a reward class of size $N$ improves from $\\log N$ to $\\log N/\\log k$. We further show that these two effects can be separated. Under robust evaluation, where one learned policy must compete with the demonstrator simultaneously for every reward in the class, the fast $1/\\varepsilon$ dependence persists, while the $1/\\log k$ improvement can disappear. We establish matching upper and lower bounds in the corresponding regimes and give a greedy multiplicative-weights learner achieving the upper bounds without any assumption on demonstrator quality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33291",
  "author_total": 2,
  "authors": [
    {
      "name": "Chandramauli Chakraborty"
    },
    {
      "name": "Cong Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1qptgnht49v2s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33291",
  "fulltext_url": null,
  "id": "1qptgnht49v2s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33291",
  "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.IT"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1702|Reinforcement Learning in Robotics"
    ]
  ],
  "openalex": "W7214786686",
  "pdf_url": "https://arxiv.org/pdf/2609.33291",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1qptgnht49v2s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2609.33291",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33291"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "The Statistical Benefits of Multiple Responses for Learning from Demonstrations",
  "title_text": "The Statistical Benefits of Multiple Responses for Learning from Demonstrations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:42Z",
  "url": "https://research.draconitic.com/paper/1qptgnht49v2s",
  "venue": "arXiv",
  "versions": []
}