{
  "abstract": "How far can stochastic gradient descent ascent (SGDA) go by tuning its timescale ratio and step sizes in nonconvex min-max games? We answer this question for nonconvex-PŁ (NC-PŁ) games by establishing the first tight complexity of two-timescale SGDA with a fixed timescale ratio and non-increasing step sizes. For $\\ell$-smooth games with an inner $μ$-PŁ inequality, we prove a complexity lower bound $Ω(κ^2\\ell\\varepsilon^{-2}+κ^4\\ellσ^2\\varepsilon^{-4})$, where $κ=\\ell/μ$ is the condition number, $σ^2$ is the gradient variance, and $\\varepsilon$ measures the outer gradient norm. This matches existing SGDA upper bounds and establishes a complexity separation from Smoothed-AGDA (Yang et al., 22'). In addition, we show that SGDA can fail to find a stationary point when its timescale ratio is as small as $o(κ^2)$. Our negative results highlight the fundamental limitation of SGDA in NC-PŁ games, and justify the development of alternative methods.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07814",
  "author_total": 1,
  "authors": [
    {
      "name": "Junsoo Ha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1dwhcfm1gv6cd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07814",
  "fulltext_url": null,
  "id": "1dwhcfm1gv6cd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07814",
  "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",
      "cs.GT"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7221010648",
  "pdf_url": "https://arxiv.org/pdf/2610.07814",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1dwhcfm1gv6cd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:26Z",
      "native_id": "2610.07814",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07814"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Stochastic Gradient Descent Ascent is Suboptimal for Nonconvex-PŁ Min-Max Games",
  "title_text": "Stochastic Gradient Descent Ascent is Suboptimal for Nonconvex-PŁ Min-Max Games",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/1dwhcfm1gv6cd",
  "venue": "arXiv",
  "versions": []
}