{
  "abstract": "We study online convex optimization with one unbiased stochastic subgradient per round and an unknown finite conditional $p$th noise moment, $1<p\\le2$. For every fixed interval $I$ of length $n$ and comparator path with $Λ_I=1+P_I/D$, one learner achieves \\[ E[Regret_I(u)]\\le\\min(GDn, C[GD\\sqrt{n(Λ_I+\\log^2(2T))} +σDn^{1/p}(Λ_I+\\log^2(2T))^{(p-1)/p}]). \\] The learner uses none of $G,σ,p,I,P_I$, and the constant is universal. Interval adaptation adds to comparator complexity, preserving the distinct mean-gradient and noise exponents. The analysis controls calibration in expectation and limits the cost of observation-scale changes. Its general theorem compares to distributions over predictably available experts with relative-entropy dependence on a nonuniform prior. A common prior favors long windows and long restart lengths. With the statistics supplied, the interval cost becomes $1+\\log(T/n)$, including the optimal full-horizon static rate. A change-of-measure lower bound identifies the noise power of this logarithm for learners retaining a full-horizon optimal guarantee, under explicit conditions. Static comparisons and deterministic partitions follow from the same decisions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02258",
  "author_total": 1,
  "authors": [
    {
      "name": "Vaneet Aggarwal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6ha89pj261h5r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02258",
  "fulltext_url": null,
  "id": "6ha89pj261h5r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02258",
  "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.IT"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7220388789",
  "pdf_url": "https://arxiv.org/pdf/2610.02258",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6ha89pj261h5r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02258",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02258"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Parameter-Free Interval-Dynamic Regret under Heavy-Tailed Noise",
  "title_text": "Parameter-Free Interval-Dynamic Regret under Heavy-Tailed Noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/6ha89pj261h5r",
  "venue": "arXiv",
  "versions": []
}