{
  "abstract": "We develop an accelerated stochastic method for convex $(H_0,H_1)$-smooth optimization under heavy-tailed noise. The unbiased oracle has a finite $p$-th noise moment, $1<p\\le2$, with constant, gradient-dependent, and gap-dependent terms. Our method combines accelerated updates with clipping, projection, and phase restarts. Each iteration uses a single stochastic-gradient sample, without minibatching. We prove high-probability convergence to any desired accuracy despite clipping bias. The deterministic terms retain square-root dependence on both $H_0$ and $H_1$. In our three-component noise model, strong convexity leaves a polynomial accuracy cost only for the constant component; without it, the dependence is logarithmic even for $p<2$. More generally, for noise moments scaling as $(f(x)-f^\\star)^α$, the stochastic cost becomes logarithmic at $α=p$ for convex objectives and $α=p/2$ under strong convexity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33415",
  "author_total": 3,
  "authors": [
    {
      "name": "Aleksandr Lobanov"
    },
    {
      "name": "Darina Dvinskikh"
    },
    {
      "name": "Alexander Gasnikov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1a1s2rtb0gspf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33415",
  "fulltext_url": null,
  "id": "1a1s2rtb0gspf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33415",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7214721777",
  "pdf_url": "https://arxiv.org/pdf/2609.33415",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1a1s2rtb0gspf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33415",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33415"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Accelerated Stochastic Method under $(H_0,H_1)$-Smoothness and Heavy-Tailed Noise",
  "title_text": "Accelerated Stochastic Method under (H_0,H_1)-Smoothness and Heavy-Tailed Noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/1a1s2rtb0gspf",
  "venue": "arXiv",
  "versions": []
}