{
  "abstract": "We study learning in zero-sum games with delayed feedback. We introduce Multi-Anchor Optimistic Online Mirror Descent (MAO-OMD), a single algorithm which obtains optimal fast rates in self-play on smooth games, while simultaneously maintaining minimax optimal guarantees against arbitrary opponents. In particular, in smooth zero-sum games with arbitrary and unknown feedback delays, MAO-OMD obtains $O(σ_{\\max}+1)$ social and individual regrets when used by both players, where $σ_{\\max}$ denotes the maximum number of outstanding gradients, while also guaranteeing minimax optimal $O(\\sqrt{T+d_{\\mathrm{tot}}})$ individual regret against arbitrary opponents, where $d_{\\mathrm{tot}}$ is the total delay. Moreover, we show that these optimal rates cannot be obtained simultaneously using the standard black-box reduction to the undelayed setting. We also extend our results to multi-player games, and to games with player-dependent delay sequences.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07773",
  "author_total": 5,
  "authors": [
    {
      "name": "Emmanuel Esposito"
    },
    {
      "name": "Andrew Jacobsen"
    },
    {
      "name": "Hao Qiu"
    },
    {
      "name": "Alexander Ryabchenko"
    },
    {
      "name": "Mengxiao Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e2q2akpks2e8a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07773",
  "fulltext_url": null,
  "id": "e2q2akpks2e8a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07773",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07773",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e2q2akpks2e8a.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:40Z",
      "native_id": "2611.07773",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07773"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Optimal Learning in Games with Arbitrary Delays: Best-of-Both-Worlds for Self-Play and Adversarial Opponents",
  "title_text": "Optimal Learning in Games with Arbitrary Delays: Best-of-Both-Worlds for Self-Play and Adversarial Opponents",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:52Z",
  "url": "https://research.draconitic.com/paper/e2q2akpks2e8a",
  "venue": "arXiv",
  "versions": []
}