{
  "abstract": "We characterize, up to logarithmic factors, the minimax expected query complexity of finite-sum nonconvex-strongly-concave optimization under mean-squared averaged smoothness. For randomized zero-respecting incremental first-order algorithms, the complexity is $\\tildeΘ(n+\\min\\{\\sqrt{n}\\,κ,n^{3/4}\\sqrtκ\\}\\,LΔ\\varepsilon^{-2})$ throughout $κ=L/μ\\ge1$, under exact dual initialization and for $0<\\varepsilon^2\\le c_0LΔ$, where $c_0>0$ is universal. This characterization is our main result. A dual-chain construction provides the lower bound and matches the existing Catalyst upper bound for $κ\\ge\\sqrt{n}$. For $1\\leκ\\le\\sqrt{n}$, we introduce recursive proximal descent-ascent (RPDA), which retains a recursive gradient estimator across proximal subproblems and attains $\\tilde{O}(n+\\sqrt{n}\\,κLΔ\\varepsilon^{-2})$ with a fixed query budget. Both upper bounds guarantee an expected squared primal gradient at most $\\varepsilon^2$. Under individual smoothness, we also prove $Ω(n+\\min\\{κ,\\sqrt{nκ}\\}\\,LΔ\\varepsilon^{-2})$ for every $κ\\ge1$. It matches the polynomial upper rate for a bilinear subclass when $κ\\ge n$; the intermediate-condition-number gap remains open.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04944",
  "author_total": 1,
  "authors": [
    {
      "name": "Qihao Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/13fgv4556m0jk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04944",
  "fulltext_url": null,
  "id": "13fgv4556m0jk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04944",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7220682950",
  "pdf_url": "https://arxiv.org/pdf/2610.04944",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/13fgv4556m0jk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04944",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04944"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Near-Optimal Complexity of Finite-Sum Nonconvex-Strongly-Concave Minimax Optimization",
  "title_text": "Near-Optimal Complexity of Finite-Sum Nonconvex-Strongly-Concave Minimax Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/13fgv4556m0jk",
  "venue": "arXiv",
  "versions": []
}