{
  "abstract": "We study online convex optimization with one unbiased stochastic subgradient per round and noise having a finite $p$-th central moment, where $p\\in(1,2]$ is unknown. For a bounded convex domain of diameter $D$, subgradients bounded by $G$, noise scale $σ$, and comparator path length $P_T$, let $Λ_T=1+P_T/D$. A single algorithm, using none of $G,σ,p,P_T$, attains expected dynamic regret $O_p\\left(\\min\\{GD\\sqrt{TΛ_T}+σDT^{1/p}Λ_T^{(p-1)/p},\\,GDT\\}\\right)$ against every fixed comparator sequence. Restarted AdaGrad experts produce the noise-path exponent $(p-1)/p$, and a prior favoring longer restart intervals removes horizon-dependent logarithmic overhead. We give an explicit bound uniform in $p$; its logarithm-free form has noise coefficient $O(1+\\log(p/(p-1)))$, while the static-regret constant is universal. The analysis requires only marginal noise moments and permits dependent errors. Complete pathwise proofs retain both the expert-loss range and the gradient energies preceding comparator movement. Matching lower bounds hold on every bounded convex domain of positive diameter, under the same gradient-only information model. Together with a path-budget-tuned upper bound, they characterize the minimax rate with universal constants, including its linear-regret saturation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.27073",
  "author_total": 1,
  "authors": [
    {
      "name": "Vaneet Aggarwal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/21sw35z93n8nn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.27073",
  "fulltext_url": null,
  "id": "21sw35z93n8nn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.27073",
  "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.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7171806280",
  "pdf_url": "https://arxiv.org/pdf/2607.27073",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/21sw35z93n8nn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2607.27073",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.27073"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Parameter-Free Dynamic Regret under Heavy-Tailed Noise",
  "title_text": "Parameter-Free Dynamic Regret under Heavy-Tailed Noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/21sw35z93n8nn",
  "venue": "arXiv",
  "versions": []
}