{
  "abstract": "Saddle-point problems play an important role in modern machine learning, including robust optimization and algorithmic fairness. We investigate structured convex--concave minimax problems where the primal variable lies in a high-dimensional, unconstrained space $\\mathbb{R}^d$, while the dual variable is confined to a constrained, low-dimensional space $\\mathbb{R}^J$, with $J\\ll d$. Although existing theoretical frameworks establish that an accelerated rate of $\\mathcal{O}(L/T^2)$ is possible, solving the associated subproblems efficiently can become a computational bottleneck in high dimensions. To address this, we introduce a decoupling technique. By restricting second-order updates to the low-dimensional dual space and employing first-order methods in the high-dimensional primal space, our framework combines Newton methods with Nesterov acceleration. For simplex-constrained dual variables and regularizers compatible with a self-concordant barrier, the resulting algorithm achieves a convergence rate of $\\mathcal{O}(L/T^2)$ in primal objective suboptimality after $T$ outer iterations, without strong dual concavity. The additional linear-algebra cost per outer iteration is $\\widetilde{\\mathcal{O}}(dJ^2+J^{3.5})$, alongside one evaluation of the component losses and their Jacobian.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36997",
  "author_total": 3,
  "authors": [
    {
      "name": "Clement Lezane"
    },
    {
      "name": "Sophie Langer"
    },
    {
      "name": "Wouter M. Koolen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7a2gngehbk2bd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36997",
  "fulltext_url": null,
  "id": "7a2gngehbk2bd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36997",
  "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": "W7214919712",
  "pdf_url": "https://arxiv.org/pdf/2609.36997",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7a2gngehbk2bd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36997",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36997"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Acceleration for Affine-coupling problems",
  "title_text": "Acceleration for Affine-coupling problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/7a2gngehbk2bd",
  "venue": "arXiv",
  "versions": []
}