{
  "abstract": "Variational inequalities (VIs) provide a unified framework for optimization, saddle-point, equilibrium, and learning problems, where operators need not be globally Lipschitz. The $α$-symmetric generalized-smoothness condition allows local operator variation to grow with the operator norm, but existing extragradient methods often require unknown problem-specific constants. To address this issue, we propose PF-AEG, an explicit, line-search-free extragradient method whose stepsizes use quantities generated during the iterations, without prior knowledge of these constants. Under $p$-quasi-sharpness, we prove full-sequence convergence and last-iterate squared-distance rates: linear convergence for $0<p\\le2$ and $\\mathcal{O}(k^{-2/(p-2)})$ for $p>2$. The latter matches existing parameter-dependent rates under comparable assumptions, while the linear guarantee extends the previous $p=2$ result to $0<p\\le2$. Building on the idea of PF-AEG, we develop AEG-VR, a variance-reduced adaptive extragradient method for finite-sum VIs. We prove almost-sure convergence and, under mild conditions, obtain analogous expected last-iterate rates, while retaining independence from the unknown problem-specific constants in stepsize selection. Experiments on synthetic generalized-smooth VIs and several learning problems show that the proposed methods are competitive with, and in several tested regimes outperform, existing baselines.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14839",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhaoyang Chu"
    },
    {
      "name": "Hongwei Liu"
    },
    {
      "name": "Yakui Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1g6aydpc8qzvh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14839",
  "fulltext_url": null,
  "id": "1g6aydpc8qzvh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14839",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7221754469",
  "pdf_url": "https://arxiv.org/pdf/2610.14839",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1g6aydpc8qzvh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14839",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14839"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Parameter-Free Adaptive Extragradient Methods for Generalized-Smooth Variational Inequalities",
  "title_text": "Parameter-Free Adaptive Extragradient Methods for Generalized-Smooth Variational Inequalities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/1g6aydpc8qzvh",
  "venue": "arXiv",
  "versions": []
}