{
  "abstract": "Gradient clipping is widely used to stabilize training, but it need not improve the statistical accuracy of averaged SGD, even under heavy-tailed noise. We derive a finite-sample comparison of clipped and unclipped Polyak-Ruppert averaged SGD under finite conditional $p$-th moments, $p\\ge2$. Our main result gives explicit accuracy and confidence conditions under which, for $p>2$, the Gaussian term dominates the unclipped deviation bound, so clipping need not improve its leading order. By balancing clipping bias and concentration, we obtain a bound in which the heavy-tail correction depends logarithmically rather than polynomially on the inverse failure probability. At $p=2$, this improves the confidence dependence of the leading bound. We establish sharpness of the unclipped heavy-tail term through an exact one-dimensional quadratic recursion and extend the comparison to projected convex SGD. We also prove concrete costs of clipping: every fixed finite threshold increases asymptotic variance on a scalar Gaussian quadratic, while whole-gradient clipping can shift the limiting point under asymmetric noise.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32962",
  "author_total": 8,
  "authors": [
    {
      "name": "Alexandra Suvorikova"
    },
    {
      "name": "Egor Gladin"
    },
    {
      "name": "Darina Dvinskikh"
    },
    {
      "name": "Artem Agafonov"
    },
    {
      "name": "Mohammad Alkousa"
    },
    {
      "name": "Yuriy Dorn"
    },
    {
      "name": "Vladislav Matyukhin"
    },
    {
      "name": "Alexander Gasnikov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ey58zmrbmn5tf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32962",
  "fulltext_url": null,
  "id": "ey58zmrbmn5tf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32962",
  "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.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7214746261",
  "pdf_url": "https://arxiv.org/pdf/2609.32962",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ey58zmrbmn5tf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32962",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32962"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Clipped or Unclipped? Finite-Sample Trade-offs for Averaged SGD under Heavy-Tailed Noise",
  "title_text": "Clipped or Unclipped? Finite-Sample Trade-offs for Averaged SGD under Heavy-Tailed Noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/ey58zmrbmn5tf",
  "venue": "arXiv",
  "versions": []
}