{
  "abstract": "Thompson sampling (TS) achieves logarithmic and asymptotically optimal regret in classical stochastic bandits, but its behavior in multi-agent learning remains less understood. We study TS in an unknown finite two-player zero-sum matrix game with Gaussian bandit feedback. Under centralized self-play, TS samples a single payoff matrix from the posterior and plays a Nash equilibrium of the sampled game. For every fixed zero-sum game with a unique Nash equilibrium, we show that the expected cumulative duality gap is $O(\\sqrt T)$. The rate improves to $O(\\log T)$ for pure equilibria. We then identify the exact coefficient of the $\\sqrt T$ term, which depends only on the equilibrium strategies and the noise level. We also establish a minimax lower bound matching the square-root dependence on $T$ and an instance-dependent lower bound matching the logarithmic dependence on $T$ for a class of games with a unique pure equilibrium. Experiments support the predicted rates and coefficient.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18899",
  "author_total": 3,
  "authors": [
    {
      "name": "Kenshi Abe"
    },
    {
      "name": "Kaito Ariu"
    },
    {
      "name": "Po-An Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fc1wv8pfrmwk7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18899",
  "fulltext_url": null,
  "id": "fc1wv8pfrmwk7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18899",
  "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.GT"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7221887380",
  "pdf_url": "https://arxiv.org/pdf/2610.18899",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fc1wv8pfrmwk7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:42Z",
      "native_id": "2610.18899",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18899"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Thompson Sampling for Learning in Zero-Sum Games",
  "title_text": "Thompson Sampling for Learning in Zero-Sum Games",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:42Z",
  "url": "https://research.draconitic.com/paper/fc1wv8pfrmwk7",
  "venue": "arXiv",
  "versions": []
}