{
  "abstract": "Stochastic Gradient Langevin Dynamics (SGLD) reduces the cost of Langevin-based sampling by replacing full-dataset drift evaluations with mini-batch approximations, but the resulting subsampling error may offset this computational saving. We study this trade-off for stochastic differential equations with finite-sum drifts and compare the computational cost of SGLD with that of the Euler-Maruyama (EM) method. For a prescribed mean-square accuracy $\\varepsilon^2$, we derive complexity estimates that explicitly track the dependence on the dataset size $m$, mini-batch size $s$, and accuracy parameter $\\varepsilon$. The resulting comparison reveals distinct parameter regimes in which either method is preferable. In particular, EM can have lower leading-order cost only in a small-data, aggressive-subsampling regime, whereas SGLD is favoured over most of the remaining parameter space. In the practically relevant regime $s \\ll m$, the transition between the two methods occurs at the scale $m \\asymp \\varepsilon^{-1}$. We complement the theoretical analysis with numerical experiments based on a Gaussian Bayesian inference model, which examine the predicted cost regimes together with the underlying discretisation error and variance estimates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17750",
  "author_total": 5,
  "authors": [
    {
      "name": "Mateusz B. Majka"
    },
    {
      "name": "Tigran Nagapetyan"
    },
    {
      "name": "Łukasz Szpruch"
    },
    {
      "name": "Yue Wu"
    },
    {
      "name": "Danqi Zhuang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4d69dan3aafrn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17750",
  "fulltext_url": null,
  "id": "4d69dan3aafrn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17750",
  "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.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7213508745",
  "pdf_url": "https://arxiv.org/pdf/2609.17750",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4d69dan3aafrn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.17750",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17750"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.CO",
      "subfield": "statistics"
    }
  ],
  "title": "On the computational cost of Stochastic Gradient Langevin Dynamics",
  "title_text": "On the computational cost of Stochastic Gradient Langevin Dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:10Z",
  "url": "https://research.draconitic.com/paper/4d69dan3aafrn",
  "venue": "arXiv",
  "versions": []
}