{
  "abstract": "For $(Q_t,P_t)$ governed by suitably damped underdamped Langevin dynamics, we quantify the convergence in KL divergence of the positional marginal to a $σ$-strongly log-concave target $π(dq) = \\frac{1}{Z}e^{-V(q)}dq$ as \\begin{align*} \\operatorname{KL}(\\operatorname{Law}(Q_t) \\| π) \\leq e^{-\\sqrtσ t}\\operatorname{KL}(\\operatorname{Law}(Q_{0}, P_{0})\\, \\|\\, Π_0), \\end{align*} where $Π_0$ denotes an appropriately selected reference measure. When $π$ is merely log-concave, the estimate \\begin{align*} \\operatorname{KL}(\\operatorname{Law}(Q_t) \\| π) \\leq \\frac{τ^2}{t^2}\\operatorname{KL}(\\operatorname{Law}(Q_τ, P_τ)\\, \\|\\, Π_τ) \\end{align*} is derived, where $Π_τ$ denotes another correspondingly chosen reference measure at time $τ> 0$. Both rates match precisely the canonical rates of the corresponding accelerated gradient flows in $\\mathbb{R}^d$. They are achieved by the novel interpretation of the underdamped Langevin dynamics as a combination of strategies in an online sampling game and by estimating the KL divergence using a cost function informed by fictitious competitors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07812",
  "author_total": 2,
  "authors": [
    {
      "name": "Alexandra Borkowski"
    },
    {
      "name": "Nikolas Nüsken"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a0f7hx4b890vk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07812",
  "fulltext_url": null,
  "id": "a0f7hx4b890vk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07812",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7212017251",
  "pdf_url": "https://arxiv.org/pdf/2609.07812",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a0f7hx4b890vk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07812",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07812"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The Fenchel Game of Underdamped Langevin Dynamics: Insights into Accelerated Convergence",
  "title_text": "The Fenchel Game of Underdamped Langevin Dynamics: Insights into Accelerated Convergence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/a0f7hx4b890vk",
  "venue": "arXiv",
  "versions": []
}