{
  "abstract": "We study the deterministic oracle complexity of smooth convex optimization when the algorithm receives only exact function values. The objective is a globally $β$-smooth convex function, all queries and the final output are restricted to the Euclidean ball of radius $R$, and the unique minimizer lies in the ball of radius $R/2$. We establish an upper bound of $O(d\\sqrt{βR^2/ε})$ using coordinate finite differences together with an error-robust accelerated projected method. Our main contribution is a matching lower bound, up to the high-accuracy saturation of the construction: any deterministic adaptive value-oracle algorithm requires $Ω\\!\\left(d\\min\\{\\sqrt{βR^2/ε},(d/\\log(ed))^{1/3}\\}\\right)$ queries. Consequently, the minimax oracle complexity is $Θ(d\\sqrt{βR^2/ε})$ throughout the moderate-accuracy regime $βR^2(\\log(ed)/d)^{2/3}\\leqε\\leq cβR^2$ for a universal constant $c>0$. The lower bound must account for the fact that a single exact real value can encode arbitrarily much information. To overcome this difficulty, we construct a single fixed smooth convex hard instance using a Moreau-smoothed biased max chain, an exact prefix-shielding mechanism, and batched delayed rotations. These techniques preserve consistency with the full adaptive transcript and establish the optimality of the square-root complexity branch for deterministic bounded-query algorithms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18230",
  "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/7fxkvn86gd658.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18230",
  "fulltext_url": null,
  "id": "7fxkvn86gd658",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18230",
  "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": "W7213563842",
  "pdf_url": "https://arxiv.org/pdf/2609.18230",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7fxkvn86gd658.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2609.18230",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18230"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Near-Optimal Deterministic Exact-Value Complexity for Smooth Convex Optimization",
  "title_text": "Near-Optimal Deterministic Exact-Value Complexity for Smooth Convex Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/7fxkvn86gd658",
  "venue": "arXiv",
  "versions": []
}