{
  "abstract": "We study a variant of the Thompson Sampling (TS) algorithm, called $α$-TS, for solving stochastic generalized linear bandit problems. Existing analyses of TS require inflating the posterior variance to derive near-optimal regret guarantees. We formalize the idea of variance inflation by introducing $α$-TS that uses a fractional or $α$-posterior instead of the standard posterior. Our main contribution is to identify general regularity conditions on the prior and reward distributions that enable a regret analysis of $α$-TS without assuming any tractable approximation of the posterior distribution, unlike previous works. For a specific choice of $α\\propto d^{-1}$, our general regret bound yields the best known regret bound of $O(d^{3/2}\\sqrt{T}\\log T)$ for both the exponential and sub-Gaussian families of reward distributions. We further provide an $α$-dependent lower bound showing that the regret constant depends on the product $αd$, and that when $α\\propto d^{-1}$ the regret scales as $Ω(d^{3/2}\\sqrt{T})$, explaining the origin of the $d^{3/2}$ factor in the upper bound. Our proof technique adapts and combines recent advancements in the analysis of linear bandit problems with first- and second-order posterior concentration theory from the Bayesian statistics literature.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01999",
  "author_total": 4,
  "authors": [
    {
      "name": "Prateek Jaiswal"
    },
    {
      "name": "Debdeep Pati"
    },
    {
      "name": "Anirban Bhattacharya"
    },
    {
      "name": "Bani K. Mallick"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cx7xsk514wzmj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01999",
  "fulltext_url": null,
  "id": "cx7xsk514wzmj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01999",
  "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",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7207627689",
  "pdf_url": "https://arxiv.org/pdf/2609.01999",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cx7xsk514wzmj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.01999",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01999"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Posterior Tempering Explains Variance Inflation in Linear and Generalized Linear Thompson Sampling",
  "title_text": "Posterior Tempering Explains Variance Inflation in Linear and Generalized Linear Thompson Sampling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:26Z",
  "url": "https://research.draconitic.com/paper/cx7xsk514wzmj",
  "venue": "arXiv",
  "versions": []
}