{
  "abstract": "Combinatorial Thompson sampling (CTS) draws independent posterior samples for every arm, so its exploration dynamics ignore any relation among arms. We study a minimal change to those dynamics: an LLM is queried once for a partition of the arms, the partition becomes a positive-definite correlation matrix $Σ$ through an RBF kernel on cluster ranks, and the per-round posterior sample is drawn with covariance $Σ$ while the Beta posteriors are updated from real rewards only, so the LLM shapes how the sampler moves, not what it believes. We give a self-contained Bayesian regret bound for the idealized Gaussian sampler whose information gain splits into a $K\\log T$ term from the $K$-cluster structure and a ridge term that grows to $d\\log T$: the $\\sqrt{d/K}$ improvement over independent sampling is a finite-horizon transient, exact only as the within-cluster correlation tends to one. The correlated sampler reduces regret by 19% over CTS on 16 synthetic Bernoulli families at $T=2{,}500$ (6-7% at $T=25{,}000$ with data-adaptive kernels) and by 41% on the Microsoft MIND-small news benchmark ($d=200$ real articles), while pseudo-observation warm starts give nothing. An LLM-free ablation with a simulated oracle of controlled quality shows that on unstructured instances the gain is a property of the kernel shape (a random partition, or a plain tempering of the sampling noise, reproduces it), while belief injection at matched oracle quality never helps.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07470",
  "author_total": 3,
  "authors": [
    {
      "name": "Vikram Kakaria"
    },
    {
      "name": "Anish Kataria"
    },
    {
      "name": "Anany Kotawala"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e1sads0tqf1ts.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07470",
  "fulltext_url": null,
  "id": "e1sads0tqf1ts",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07470",
  "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.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7220910403",
  "pdf_url": "https://arxiv.org/pdf/2610.07470",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e1sads0tqf1ts.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:32Z",
      "native_id": "2610.07470",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07470"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Structure, Not Belief: Correlated Thompson Sampling from LLM-Derived Covariance in Combinatorial Semi-Bandits",
  "title_text": "Structure, Not Belief: Correlated Thompson Sampling from LLM-Derived Covariance in Combinatorial Semi-Bandits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:32Z",
  "url": "https://research.draconitic.com/paper/e1sads0tqf1ts",
  "venue": "arXiv",
  "versions": []
}