{
  "abstract": "Stochastic min-max optimization has attracted increasing attention due to its applications in modern machine learning, while existing theoretical studies mainly rely on the bounded variance assumption for stochastic gradients. Under heavy-tailed noise, where stochastic gradients only possess a finite $p$-th moment for $p\\in(1,2]$, gradient clipping or normalization is commonly believed to be necessary to guarantee convergence. In this work, we revisit stochastic min-max optimization under heavy-tailed noise and provide a comprehensive theoretical study of stochastic gradient descent ascent (SGDA). We first show that vanilla SGDA, without any modification to its update rule, can converge under heavy-tailed noise in both nonconvex-strongly-concave (NC-SC) and nonconvex-concave (NC-C) settings, establishing the first convergence guarantees for SGDA in these regimes. Beyond unregularized problems, we further investigate regularized stochastic min-max optimization, where directly incorporating gradient normalization into proximal updates is nontrivial due to the incompatibility between normalization and proximal structures. We overcome this difficulty by developing new clipping-free algorithms, i.e., Stoc-TRGDAM and Stoc-TRGDmax, and they both can achieve the optimal dependence on the target accuracy without using gradient clipping.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06064",
  "author_total": 3,
  "authors": [
    {
      "name": "Tianxi Zhu"
    },
    {
      "name": "Yi Xu"
    },
    {
      "name": "Xiangyang Ji"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5m34ypwwt163z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06064",
  "fulltext_url": null,
  "id": "5m34ypwwt163z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06064",
  "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.AI"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7212058291",
  "pdf_url": "https://arxiv.org/pdf/2609.06064",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5m34ypwwt163z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06064",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06064"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "The Role of Gradient Modification in Heavy-Tailed Nonconvex Stochastic Min-Max Optimization",
  "title_text": "The Role of Gradient Modification in Heavy-Tailed Nonconvex Stochastic Min-Max Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:07Z",
  "url": "https://research.draconitic.com/paper/5m34ypwwt163z",
  "venue": "arXiv",
  "versions": []
}