{
  "abstract": "We study adversarial linear bandits with strong corruption, in which an adaptive adversary chooses the reward vectors and a strong adversary corrupts each observed reward after seeing the learner's action, subject to a known total corruption budget $C$. Strong corruption breaks the importance-weighted reward estimates used by adversarial bandit algorithms: by corrupting only the rounds in which a rarely sampled action is drawn, the adversary amplifies each unit of corruption by the inverse of its sampling probability. The best known bound for this problem, $\\tilde O(\\sqrt{d^3T} + dC)$ by Liu et al. (2024), is a factor $\\sqrt{d}$ above the corruption-free rate in its leading term, and whether $\\tilde O(d\\sqrt{T} + dC)$ regret is achievable was left open. We propose CRW-FTRL, which runs follow-the-regularized-leader with a radius-weighted entropy regularizer and estimates rewards with a normalized kernel estimator whose sensitivity to corruption is governed by per-action radii instead of inverse sampling probabilities. The radii are nondecreasing and are chosen jointly with the sampling distribution through a monotone log-determinant barrier problem, so that a negative linear term in the regularizer cancels both the corruption bias and the estimation error of every comparator. For $K$ actions in $\\mathbb{R}^d$, CRW-FTRL achieves $\\tilde O(\\sqrt{dT\\log K} + dC)$ regret with high probability against an adaptive adversary, which matches the best known corruption-free rate and the $Ω(dC)$ lower bound up to logarithmic factors. Applied to a discretization of a general compact action set, it yields $\\tilde O(d\\sqrt{T} + dC)$ regret, which settles the statistical rate of corrupted adversarial linear bandits under strong corruption.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38243",
  "author_total": 2,
  "authors": [
    {
      "name": "Qiwei Di"
    },
    {
      "name": "Quanquan Gu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bvbb15dnf71f9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38243",
  "fulltext_url": null,
  "id": "bvbb15dnf71f9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38243",
  "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.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38243",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bvbb15dnf71f9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:41Z",
      "native_id": "2610.38243",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38243"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Nearly Minimax Optimal Regret for Adversarial Linear Bandits with Strong Corruptions",
  "title_text": "Nearly Minimax Optimal Regret for Adversarial Linear Bandits with Strong Corruptions",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:00Z",
  "url": "https://research.draconitic.com/paper/bvbb15dnf71f9",
  "venue": "arXiv",
  "versions": []
}