{
  "abstract": "We study stochastic convex optimization under asymmetric \\((L_0,L_1)\\)-generalized smoothness, a model motivated by machine-learning objectives whose local curvature may grow with the gradient norm. We assume an unbiased first-order oracle with additive norm-sub-Gaussian noise. Acceleration is difficult in this setting because momentum may enter regions of much larger curvature, while stochastic gradients cannot reliably certify an unrestricted trajectory. We propose \\textsf{ARC-SG}, a two-phase accelerated method: Phase~I reduces excessively large gradients using a generalized-smoothness-aware stochastic step, then Phase~II solves strongly convex proximal subproblems by a restarted accelerated solver confined to certified smoothness balls. Exact proximal points do not increase the gradient norm, allowing these certificates to propagate through the outer loop. The contribution is a query-by-query certified-localization construction with explicit generalized-smoothness factors and a strongly convex restart extension. \\textsf{ARC-SG} achieves, with high probability, an accelerated optimization contribution and smooth-subclass-optimal statistical dependence on accuracy, up to logarithmic and generalized-smoothness factors. Its convex accuracy exponents agree with a contemporaneous public stochastic-acceleration result under a broader smoothness and affine-variance model; our distinction is the certified geometry, explicit parameter accounting, and strongly convex guarantee. The results recover classical accelerated stochastic rates when \\(L_1=0\\). Experiments on objectives with unbounded gradients illustrate the two-phase mechanism and its finite-budget advantage.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06555",
  "author_total": 4,
  "authors": [
    {
      "name": "Darina Dvinskikh"
    },
    {
      "name": "Alexander Gasnikov"
    },
    {
      "name": "Aleksandr Lobanov"
    },
    {
      "name": "Ilgam Latypov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2vnp95zak9vft.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06555",
  "fulltext_url": null,
  "id": "2vnp95zak9vft",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06555",
  "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": "W7212074908",
  "pdf_url": "https://arxiv.org/pdf/2609.06555",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2vnp95zak9vft.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06555",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06555"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Localize, Restart, Accelerate: Stochastic Optimization under Generalized Smoothness",
  "title_text": "Localize, Restart, Accelerate: Stochastic Optimization under Generalized Smoothness",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/2vnp95zak9vft",
  "venue": "arXiv",
  "versions": []
}