{
  "abstract": "We study smooth strongly convex--strongly concave minimax optimization in the deterministic unconstrained setting, without assuming a bilinear or separable structure. Although existing multi-loop methods attain near-optimal condition-number dependence, standard single-loop methods generally exhibit a substantial complexity gap. To close this gap, we propose the Single-Loop Predictor--Corrector Extragradient Method with Damped Momentum (PCE-DM), which combines an extragradient prediction--correction scheme with a novel auxiliary feedback recursion for the weaker-curvature variable. PCE-DM uses fixed parameters and two new full-gradient evaluations per iteration after one initialization query, while requiring no inner solves, accuracy schedules, or staged restarts. We develop a Lyapunov analysis that controls the predictor--corrector mismatch through corrected-gradient increments and establish last-iterate linear convergence. Specifically, PCE-DM computes an $\\varepsilon$-accurate relative solution, measured by the squared Euclidean distance to the saddle point, within $\\mathcal{O}\\!\\left(\\sqrt{κ_xκ_y} \\log(2κ_xκ_y/\\varepsilon)\\right)$ full-gradient queries. This result closes the condition-number complexity gap between standard single-loop methods and near-optimal multi-loop methods, matching the known lower-bound order up to logarithmic factors while retaining fixed, explicit single-loop updates. Numerical experiments on regularized linear regression and AUC maximization demonstrate the computational efficiency of PCE-DM.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20327",
  "author_total": 2,
  "authors": [
    {
      "name": "Minhao Zhang"
    },
    {
      "name": "Zi Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ea29c30kp2sxc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20327",
  "fulltext_url": null,
  "id": "ea29c30kp2sxc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20327",
  "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.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7213608555",
  "pdf_url": "https://arxiv.org/pdf/2609.20327",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ea29c30kp2sxc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.20327",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20327"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Near-Optimal Single-Loop Predictor--Corrector Extragradient Method for Strongly Convex--Strongly Concave Minimax Optimization",
  "title_text": "Near-Optimal Single-Loop Predictor--Corrector Extragradient Method for Strongly Convex--Strongly Concave Minimax Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/ea29c30kp2sxc",
  "venue": "arXiv",
  "versions": []
}