{
  "abstract": "We establish high-probability accelerated convergence guarantees for convex $(L_0,L_1)$-smooth optimization with unbiased stochastic gradients under heavy-tailed noise, assuming a central $α$-th noise moment bounded by $σ^α$, $α\\in(1,2]$. Such guarantees are known under classical $L$-smoothness, but extending them through localization over an $O(R)$-radius ball may introduce an $e^{O(L_1R)}$ factor. We avoid this dependence in two ways. First, a two-phase scheme uses Clip-SGD to reach a low-curvature regime, after which clipped stochastic similar triangles (Clip-SSTM) attains, with probability at least $1-δ$, $f(y_K)-f^\\star\\le\\widetilde{\\mathcal O}\\big(L_0R^2/K^2+σRK^{-(α-1)/α}\\big),$ where $R$ bounds the distance from the Phase-II starting point to a minimizer. Second, a modified deterministic weight schedule allows Clip-SSTM to start directly from the initial point, controlling the high-curvature transient before recovering acceleration. With the prescribed initialization, both approaches recover the classical accelerated rate, with $L_1$ confined to an accuracy-independent transient, up to logarithmic factors. The two-phase analysis uses two coupled potentials to preserve the low-curvature regime despite momentum; the one-phase analysis controls the initial high-curvature regime using a modified version of the classical SSTM weight schedule.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23301",
  "author_total": 2,
  "authors": [
    {
      "name": "Taha El Bakkali El Kadi"
    },
    {
      "name": "Eduard Gorbunov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fvhyxjvztqx90.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23301",
  "fulltext_url": null,
  "id": "fvhyxjvztqx90",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23301",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7222945143",
  "pdf_url": "https://arxiv.org/pdf/2610.23301",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fvhyxjvztqx90.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.23301",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23301"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Acceleration Survives Heavy Tails and Generalized Smoothness",
  "title_text": "Acceleration Survives Heavy Tails and Generalized Smoothness",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/fvhyxjvztqx90",
  "venue": "arXiv",
  "versions": []
}