{
  "abstract": "We prove a sharp Gaussian approximation for the invariant law of constant-stepsize SGD with bounded additive noise generated by an exogenous uniformly ergodic Markov chain. For a smooth, strongly convex objective with a Lipschitz Hessian and nondegenerate long-run noise covariance, the centered iterate normalized by the square root of the stepsize is $O(\\sqrtα)$-close in 1-Wasserstein distance to its limiting Gaussian. The proof combines blockwise Gaussian comparison with long-run contraction. A four-state example gives a matching lower bound although the one-time noise marginal is symmetric and every nonzero-lag autocovariance vanishes. In this example, an adjacent third-order mixed moment produces the leading correction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39144",
  "author_total": 1,
  "authors": [
    {
      "name": "Junghoon Seo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/czbh29a89mw5g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39144",
  "fulltext_url": null,
  "id": "czbh29a89mw5g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39144",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7215086941",
  "pdf_url": "https://arxiv.org/pdf/2609.39144",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/czbh29a89mw5g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2609.39144",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39144"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Sharp Stationary Gaussian Approximation for Constant-Stepsize SGD",
  "title_text": "Sharp Stationary Gaussian Approximation for Constant-Stepsize SGD",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/czbh29a89mw5g",
  "venue": "arXiv",
  "versions": []
}