{
  "abstract": "We study stochastic convex optimization, where each sampled function can be evaluated at two arbitrary points. Our accelerated method chooses step sizes, batch sizes and smoothing radii from function values. A forward difference between smoothing scales controls the radius; we account for changes in the smoothed objective. Under the stated regularity and second-moment assumptions, exact function evaluations give \\begin{multline*} \\mathbb{E}\\bigl[f(x_N)-f(x^\\star)\\bigr] \\le \\widetilde{O}\\biggl( \\frac{\\sqrt{d}\\,M_2 D}{\\sqrt{T}} +\\min\\biggl( \\frac{L D^2}{N^2},\\; \\frac{d^{1/4} M D}{N}+\\frac{\\sqrt{d}\\,M D^2}{γ_{\\max} N^2} \\biggr)\\biggr). \\end{multline*} Here $N,T,d,D$ denote the numbers of optimization steps and paired evaluations, the dimension and a feasible-set diameter bound, respectively. Evaluations are available within Euclidean distance $γ_{\\max}$ of the feasible set. For the population objective $f(x)=\\mathbb{E}_ξ F(x,ξ)$, $M$ satisfies $|f(x)-f(y)|\\le M\\|x-y\\|_2$, and $M_2$ satisfies $\\mathbb{E}_ξ\\|\\nabla F(x,ξ)\\|_2^2\\le M_2^2$ for sample weak gradients in the interior of the evaluation domain. The method requires no $L,M,M_2$, where $L$ is a Lipschitz constant of $\\nabla f$; set $L=+\\infty$ without smoothness. The method uses exactly $2T$ values in $3N$ sequential sampling rounds with predetermined batches, or $5N$ with batches chosen from observations. An extension selects a search radius without a supplied distance bound. Fixed radius parameters can leave nonvanishing error; suitable choices depending on the budgets yield convergence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15202",
  "author_total": 6,
  "authors": [
    {
      "name": "Yuriy Dorn"
    },
    {
      "name": "Osman Osmanov"
    },
    {
      "name": "Timofei Loginov"
    },
    {
      "name": "Nazarii Tupitsa"
    },
    {
      "name": "Darina Dvinskikh"
    },
    {
      "name": "Alexander Gasnikov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fkqb1qgjt9wep.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15202",
  "fulltext_url": null,
  "id": "fkqb1qgjt9wep",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15202",
  "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": "W7221829606",
  "pdf_url": "https://arxiv.org/pdf/2610.15202",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fkqb1qgjt9wep.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15202",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15202"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Adaptive two-points zero-order accelerated methods for stochastic convex optimization problems",
  "title_text": "Adaptive two-points zero-order accelerated methods for stochastic convex optimization problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/fkqb1qgjt9wep",
  "venue": "arXiv",
  "versions": []
}