{
  "abstract": "We study geometric moment contraction (GMC) of the constant-parameter stochastic Nesterov recursion \\[ Y_k=Θ_k+β(Θ_k-Θ_{k-1}),\\qquad Θ_{k+1}=Y_k-γG(Y_k,X_{k+1}). \\] Under mean strong monotonicity and stochastic $L^p$ Lipschitz continuity, an explicit Perron comparison proves synchronous $L^p$ contraction when $βγL_p<(1-β)(1-q_{γ,p})$. This direct criterion includes infinite-variance gradients for $1<p<2$, but its small-step regime requires $β<μ/(μ+L_p)$. A complementary power-Lyapunov argument establishes a positive, generally much smaller, step-size interval for every fixed $β<1$ and every $p>1$, using only a finite $p$th gradient moment. At $p=2$, a simpler explicit certificate gives \\[ 0<γ<\\frac{2μ(1-β)^2}{L_2^2(1-β+2β^2)}. \\] Its quadratic high-momentum scaling is a limitation of the chosen metric, not a sharp stability boundary. We quantify this loss, provide a general mean-only quadratic $S$-procedure, and exploit endpoint Lyapunov inequalities under stronger samplewise sector information. Verified endpoint certificates can be orders of magnitude less conservative than the explicit metric.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31303",
  "author_total": 1,
  "authors": [
    {
      "name": "Wei Biao Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5d68cn0dq4d2b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31303",
  "fulltext_url": null,
  "id": "5d68cn0dq4d2b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31303",
  "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",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7214615240",
  "pdf_url": "https://arxiv.org/pdf/2609.31303",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5d68cn0dq4d2b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:03Z",
      "native_id": "2609.31303",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31303"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Geometric Moment Contraction for Stochastic Nesterov Acceleration",
  "title_text": "Geometric Moment Contraction for Stochastic Nesterov Acceleration",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:03Z",
  "url": "https://research.draconitic.com/paper/5d68cn0dq4d2b",
  "venue": "arXiv",
  "versions": []
}