{
  "abstract": "We study smoothed online prediction with bounded adversarial responses. This widely studied framework bridges i.i.d. sampling and adversarial covariate selection through a smoothness parameter $\\textsf{C}_{\\textsf{cov}}$, which bounds conditional covariate densities relative to a fixed, unknown base measure. We propose \\textsc{Hedge-Cover}, an information-theoretic algorithm that achieves sublinear regret $\\widetilde{O}(\\sqrt{\\text{Pdim}(\\mathcal{F}) \\textsf{C}_{\\textsf{cov}} T})$ for function classes with bounded pseudo-dimension. The algorithm aggregates a carefully constructed family of experts using \\textsc{Hedge}, with a prior that links regret to the number of disagreements between a consistent selector and a target function. We bound this number by exploiting covariate smoothness. This answers an open problem posed in \\cite{blanchard2025agnostic} on the minimax optimal adaptive regret of the smoothed online regression problem. We establish a matching lower bound for the class of linear predictors. The main intricacy of the lower bound lies in explicitly constructing a challenging sequential covariate distribution supported on mutually orthogonal hyperplanes. This construction may be of independent technical interest. Finally, we revisit the well-specified setting and quantify the effect of response noise. For conditionally $ν^2$-subGaussian responses, we extend the existing lower bound under realizable responses by showing that the minimax expected regret is $Ω((1\\vee ν)\\sqrt{(\\textsf{C}_{\\textsf{cov}}-1)dT})$ for a function class of VC dimension $d$. A corresponding upper bound for ERM matches this dependence on $ν$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32478",
  "author_total": 2,
  "authors": [
    {
      "name": "Xuanyu Chen"
    },
    {
      "name": "Yue Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0ydm0b84mn5j2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32478",
  "fulltext_url": null,
  "id": "0ydm0b84mn5j2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32478",
  "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.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7214740723",
  "pdf_url": "https://arxiv.org/pdf/2609.32478",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0ydm0b84mn5j2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32478",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32478"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Agnostic Smoothed Online Regression with Adversarial Responses",
  "title_text": "Agnostic Smoothed Online Regression with Adversarial Responses",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/0ydm0b84mn5j2",
  "venue": "arXiv",
  "versions": []
}