{
  "abstract": "We study the stochastic first-order oracle complexity of finding $ε$-stationary points of the primal function in smooth nonconvex-strongly-concave minimax optimization. For sufficiently small $ε$, we establish lower bounds of $Ω(κLΔσ^2ε^{-4})$ under the bounded-variance assumption and $Ω(κ^{3/2}\\bar LΔσε^{-3})$ under the additional assumption of averaged smoothness. Here, $L$ and $\\bar L$ denote the smoothness and averaged-smoothness constants, respectively, $Δ$ is the initial primal gap, $σ^2$ bounds the oracle variance, and $κ=L/μ$ or $\\bar L/μ$ in the respective settings, where $μ$ is the strong-concavity parameter. Our bounded-variance lower bound improves the dependence on the condition number from $κ^{1/3}$ in previous lower bounds to $κ$, while our averaged-smoothness lower bound is the first of its kind. In both settings, the resulting lower bounds match existing upper bounds in their dependence on $κ$ and $ε$. Our proofs are based on a unified quadratic lifting construction that transfers a hardness instance for stochastic nonconvex minimization to unconstrained minimax optimization while preserving the required variance and smoothness properties.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35206",
  "author_total": 3,
  "authors": [
    {
      "name": "Siqi Zhang"
    },
    {
      "name": "Qilong Wu"
    },
    {
      "name": "Junchi Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bdkeqn4mwdsvk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35206",
  "fulltext_url": null,
  "id": "bdkeqn4mwdsvk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35206",
  "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": "W7214790376",
  "pdf_url": "https://arxiv.org/pdf/2609.35206",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bdkeqn4mwdsvk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35206",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35206"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Tight Lower Bounds for Stochastic Nonconvex-Strongly-Concave Minimax Optimization",
  "title_text": "Tight Lower Bounds for Stochastic Nonconvex-Strongly-Concave Minimax Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/bdkeqn4mwdsvk",
  "venue": "arXiv",
  "versions": []
}