{
  "abstract": "Mitigating unfair disparities in sequential decision-making is a growing concern in machine learning. We study contextual bandits under a global covariate-based Lipschitz fairness constraint, pioneered by \\cite{dwork2012fairness}, requiring individuals with similar contexts to receive similar action distributions. We show that this constraint induces a randomisation region near the decision boundary and explicitly quantify the population level cost of fairness. We further establish a canonical representation of the optimal fair policy, which reduces the fair policy design to a lower-dimensional boundary optimisation problem. We develop a lazy fair greedy algorithm that exploits fairness-induced covariate diversity under continuous contexts, with policy updates computed via finite-dimensional linear programming. For general context distributions, including discrete and mixed contexts, we propose a lazy polyhedral upper confidence bound (UCB) algorithm, whose optimistic optimisation reduces to finitely many linear programs over confidence-set vertices. Both methods satisfy fairness at every round and achieve regret of order $O(\\sqrt{T} + T^{(d-2)/(d-1)}{\\indc\\{d\\geq 4\\}})$ up to poly-logarithmic factors, where $d$ is the dimension of the contexts. A matching minimax lower bound for $\\ell_1$-based fairness establishes optimality, and reveals an unavoidable nonparametric cost of learning the decision boundary, which dominates the parametric learning cost when $d \\geq 4$. Experiments on synthetic and real data support our theoretical findings and demonstrate the practical effectiveness of our methods.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00979",
  "author_total": 5,
  "authors": [
    {
      "name": "Gengyu Xue"
    },
    {
      "name": "Fan Wang"
    },
    {
      "name": "Feiyu Jiang"
    },
    {
      "name": "Zifeng Zhao"
    },
    {
      "name": "Yi Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4h6zr6eaqnhar.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00979",
  "fulltext_url": null,
  "id": "4h6zr6eaqnhar",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00979",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00979",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4h6zr6eaqnhar.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00979",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00979"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Optimal Learning in Fairness-Aware Contextual Bandits",
  "title_text": "Optimal Learning in Fairness-Aware Contextual Bandits",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:35Z",
  "url": "https://research.draconitic.com/paper/4h6zr6eaqnhar",
  "venue": "arXiv",
  "versions": []
}