{
  "abstract": "We study optimal experimental design for multinomial logit (MNL) bandits, where an agent repeatedly selects a subset of $K$ items from a ground set of size $N$ and observes single-choice feedback. Unlike linear or generalized linear bandits, MNL bandits have a combinatorial action space, which makes classical optimal design approaches and naive optimization over all subsets computationally intractable. We propose a computationally efficient optimal design framework for MNL models that achieves both statistical efficiency and scalability through two complementary approaches: (i) an exact or certified-approximate reformulation of the design oracle as a $0$-$1$ mixed-integer linear program (MILP) with solver-certified early stopping, and (ii) a fully polynomial-time lifted design that replaces the nonlinear objective with a tractable surrogate. Using the Kiefer-Wolfowitz equivalence theorem, we establish near G-optimality guarantees and characterize the induced statistical-computational trade-offs. As an application, we develop a best assortment identification algorithm for MNL bandits with linear utilities and non-uniform revenues, and prove an instance-dependent sample complexity of $\\tilde{O}\\big(\\frac{d \\log N}{Δ^2}\\big)$, where $d$ is the feature dimension, $N$ is the number of arms, and $Δ$ is the minimum revenue gap.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.25592",
  "author_total": 2,
  "authors": [
    {
      "name": "Joongkyu Lee"
    },
    {
      "name": "Min-hwan Oh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f1vn93av4tvdn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.25592",
  "fulltext_url": null,
  "id": "f1vn93av4tvdn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.25592",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7162429106",
  "pdf_url": "https://arxiv.org/pdf/2605.25592",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f1vn93av4tvdn.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:25Z",
      "native_id": "2605.25592",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.25592"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Optimal Design for Multinomial Logit Model with Applications to Best Assortment Identification",
  "title_text": "Optimal Design for Multinomial Logit Model with Applications to Best Assortment Identification",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/f1vn93av4tvdn",
  "venue": "arXiv",
  "versions": []
}