{
  "abstract": "We study the local stability of Wasserstein gradient descent-ascent (GDA) for entropy regularized two-player zero-sum games on noncompact domains. When one or both equilibrium measures fail to satisfy a Poincaré inequality, the spectral gap arguments underlying local exponential convergence are unavailable. we show that Wasserstein GDA converges algebraically to the mixed Nash equilibrium in chi-squared divergence, provided the initial relative density is a small perturbation in $L^2$ with bounded algebraic moments. The proof has two main ingredients: a cancellation in a negative Sobolev energy estimate, and a bootstrap argument that keeps the moments bounded uniformly in time. For polynomial-tailed equilibria, we construct perturbations supported far out in the tails that survive over diffusive time scales, which gives algebraic lower bounds on the worst-case relaxation rate. We also establish analogous local algebraic stability and lower bound results for mean-field Langevin dynamics, when the equilibrium fails to satisfy a spectral gap.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35528",
  "author_total": 2,
  "authors": [
    {
      "name": "Jing An"
    },
    {
      "name": "Lihan Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4hjv684f91g37.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35528",
  "fulltext_url": null,
  "id": "4hjv684f91g37",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35528",
  "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.AP"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7223796219",
  "pdf_url": "https://arxiv.org/pdf/2610.35528",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4hjv684f91g37.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35528",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35528"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Local Algebraic Stability of Wasserstein Gradient Descent-Ascent and Mean Field Langevin Dynamics without Spectral Gap",
  "title_text": "Local Algebraic Stability of Wasserstein Gradient Descent-Ascent and Mean Field Langevin Dynamics without Spectral Gap",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/4hjv684f91g37",
  "venue": "arXiv",
  "versions": []
}