{
  "abstract": "We propose a novel stochastic cascading bandit setup where probing an ordered shortlist of $K$ out of $L$ arms incurs position-dependent costs, and the learner observes only noisy feedback regarding each arm's true output. We identify a sub-class of noise models for which the optimal shortlist can be found by sorting arms according to a per-arm score: such a score exists for both selection and ordering when the channel has no false positives, and for ordering alone (but not selection) when measurements are costless; however in general neither selection nor ordering is separable once noise and cost are both present. For the case where both selection and ordering scores exist, we provide a UCB-based algorithm with $O((L-K)\\log T)$ instance-dependent regret over a time horizon $T$, which matches an algorithm-agnostic lower bound (up to constant factors). For the more challenging scenario where scores don't exist, we develop a new algorithmic template, DP-UCB, that embeds optimism directly inside an exact dynamic program, yielding $O\\big(LK\\log T\\big)$ regret. Finally, we validate our theoretical results through extensive numerical evaluations and simulations over both synthetic and real-world datasets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29381",
  "author_total": 2,
  "authors": [
    {
      "name": "Yashaswini Kaluguri"
    },
    {
      "name": "Nikhil Karamchandani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3mefhp586qdtp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29381",
  "fulltext_url": null,
  "id": "3mefhp586qdtp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29381",
  "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",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7223241136",
  "pdf_url": "https://arxiv.org/pdf/2610.29381",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3mefhp586qdtp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:29Z",
      "native_id": "2610.29381",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29381"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Cascading Bandits with Noisy Observations: Algorithms and Regret Bounds",
  "title_text": "Cascading Bandits with Noisy Observations: Algorithms and Regret Bounds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:29Z",
  "url": "https://research.draconitic.com/paper/3mefhp586qdtp",
  "venue": "arXiv",
  "versions": []
}