{
  "abstract": "We study whether the classical momentum-based acceleration that improves the condition-number dependence of gradient descent from $κ$ to $\\sqrtκ$ for strongly convex, smooth objectives extends to Gaussian variational inference (GVI) for strongly log-concave, log-smooth target distributions. With exact Gaussian expectations, a convex composite formulation of GVI yields the classical accelerated $\\sqrtκ$ convergence rate. However, when only pointwise derivatives are available, we construct a family of strongly log-concave targets for which any randomized algorithm requires $κ^{1-o(1)}$ queries to achieve a fixed objective accuracy, even when the initial objective gap is bounded independently of $κ$. Thus curvature bounds alone cannot guarantee uniform accelerated total-query complexity. We then ask which additional structure permits acceleration and give positive examples: under a Hessian-Lipschitz assumption, variance-reduced stochastic methods yield accelerated guarantees when the Hessian variation is sufficiently small. Finally, experiments on real datasets show substantial empirical speedups from acceleration across a broad range of methods.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21020",
  "author_total": 3,
  "authors": [
    {
      "name": "Jaesung R. Park"
    },
    {
      "name": "Uijeong Jang"
    },
    {
      "name": "Yifan Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5v5y1ze43a44e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21020",
  "fulltext_url": null,
  "id": "5v5y1ze43a44e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21020",
  "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": "W7222421320",
  "pdf_url": "https://arxiv.org/pdf/2610.21020",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5v5y1ze43a44e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21020",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21020"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Acceleration and its Limits in Gaussian Variational Inference",
  "title_text": "Acceleration and its Limits in Gaussian Variational Inference",
  "type": "preprint",
  "updated_at": "2026-10-30T12:30:00Z",
  "url": "https://research.draconitic.com/paper/5v5y1ze43a44e",
  "venue": "arXiv",
  "versions": []
}