{
  "abstract": "We study the non-asymptotic convergence of Stochastic Mirror Descent (SMD) algorithm when the noisy first-order oracle is driven by dependent observations. Departing from the classical i.i.d. assumption underlying most existing guarantees, we introduce a flexible ``forgetting\" condition that accommodates geometrically or polynomially dependent sequences. Under this condition we derive explicit finite-sample accuracy bounds for the averaged SMD iterates, recovering the classical $O(1/T)$ and $O(1/\\sqrt{T})$ rates in the large- and small-initial-error regimes. We instantiate the general framework on two applications: high-dimensional linear regression with dependent regressors and nonparametric estimation of the drift function of a functional autoregressive model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41251",
  "author_total": 3,
  "authors": [
    {
      "name": "Gersende Fort"
    },
    {
      "name": "Anatoli Juditsky"
    },
    {
      "name": "Jiaming Liang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f342mr5jcsa0s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41251",
  "fulltext_url": null,
  "id": "f342mr5jcsa0s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41251",
  "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",
      "math.OC"
    ],
    [
      "arxiv",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41251",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f342mr5jcsa0s.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41251",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41251"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Stochastic Mirror Descent under Dependent Observations",
  "title_text": "Stochastic Mirror Descent under Dependent Observations",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/f342mr5jcsa0s",
  "venue": "arXiv",
  "versions": []
}