{
  "abstract": "We study deterministic adaptive optimization of globally $β$-smooth, $μ$-strongly convex functions using exact scalar function values. Queries and outputs lie in $B_2^d(R)$, and the minimizer lies in $B_2^d(R/2)$. Set $κ=β/μ$, $Q=βR^2/ε$, and $D_d=(d/\\log(ed))^{1/3}$. For sufficiently large $d$ and $0<ε\\le c_εβR^2$, the minimax value complexity $N_ε$ satisfies \\[ \\begin{aligned} N_ε&\\ge c d\\min\\{\\sqrt Q,\\sqrtκ,D_d\\},\\\\ N_ε&\\le C d\\min\\left\\{ \\sqrt Q,\\sqrtκ[1+\\log_+(Q/κ)] \\right\\}, \\end{aligned} \\] where $c,C,c_ε>0$ are universal constants and $\\log_+(t)=\\max\\{0,\\log t\\}$. The lower bound uses an exactly shielded smooth chain and batched delayed rotations; the upper bound combines finite differences, acceleration, and restart. When $\\min\\{Q,κ\\}\\le D_d^2$, these bounds match up to constants in the accuracy-dominated regime $Q\\leκ$ and at constant relative accuracy $ε=Θ(μR^2)$. For arbitrarily higher accuracy in the range $κ\\le D_d^2$, the bounds differ by at most $1+\\log(μR^2/ε)$; the optimal accuracy dependence remains unresolved in general.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18728",
  "author_total": 8,
  "authors": [
    {
      "name": "Wendao Wu"
    },
    {
      "name": "Haihan Zhang"
    },
    {
      "name": "Chenheng Zhang"
    },
    {
      "name": "Yanyi Li"
    },
    {
      "name": "Chunyuan Zheng"
    },
    {
      "name": "Cong Fang"
    },
    {
      "name": "Haoxuan Li"
    },
    {
      "name": "Zhouchen Lin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6tav981er9gzk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18728",
  "fulltext_url": null,
  "id": "6tav981er9gzk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18728",
  "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": "W7213516182",
  "pdf_url": "https://arxiv.org/pdf/2609.18728",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6tav981er9gzk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:31:00Z",
      "native_id": "2609.18728",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18728"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Near-Optimal Exact-Value Zeroth-Order Complexity for Smooth Strongly Convex Optimization",
  "title_text": "Near-Optimal Exact-Value Zeroth-Order Complexity for Smooth Strongly Convex Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:47Z",
  "url": "https://research.draconitic.com/paper/6tav981er9gzk",
  "venue": "arXiv",
  "versions": []
}