{
  "abstract": "Bandit algorithms generate data for downstream inference, but adaptive sampling biases post-bandit sample means. We analyze this bias for stable index algorithms, including UCB1 and its generalizations, and derive sharp leading-order expressions for the sample-mean bias and expected $Z$-statistic, in bandit experiments of fixed horizon $T$. Our characterization reveals the algorithmic origin of bias through a key index-function-dependent quantity, which we term effective exploration rate. For example, under UCB1, the effective exploration rate is of order $\\sqrt{\\log T}$, and the standardized bias of any arm (that is not uniquely optimal) decays at the extremely slow rate $1/\\sqrt{\\log T}$. We also show how the choice of the index function affects both regret and bias, which reveals a regret-bias trade-off: more exploratory algorithm reduces bias but increases regret. We further show how bias most severely distorts confidence intervals and hypothesis tests when the tested arm is one of the tied-optimal arms. Our sharp characterization for bias uses a novel empirical fluid approximation of the algorithm's sampling dynamics, which may be of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.01069",
  "author_total": 3,
  "authors": [
    {
      "name": "Lisu Wang"
    },
    {
      "name": "Yilun Chen"
    },
    {
      "name": "Jiaqi Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/69hxjwdwzm6aa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.01069",
  "fulltext_url": null,
  "id": "69hxjwdwzm6aa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.01069",
  "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.PR"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7172378680",
  "pdf_url": "https://arxiv.org/pdf/2608.01069",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/69hxjwdwzm6aa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2608.01069",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.01069"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Sharp Characterization of Bias in Post-Bandit Inference",
  "title_text": "Sharp Characterization of Bias in Post-Bandit Inference",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:49Z",
  "url": "https://research.draconitic.com/paper/69hxjwdwzm6aa",
  "venue": "arXiv",
  "versions": []
}