{
  "abstract": "Learning operators from sequentially collected data arises in adaptive experimental design, Bayesian optimization, and dynamical-system modelling, where observations may be dependent, and future inputs or sensing operators may depend on preceding data. We derive time-uniform self-normalized concentration bounds for stochastic processes in Hilbert spaces with vector-valued noise. We use these bounds to obtain regression-error guarantees for linear operators, including targets outside the Hilbert estimation space, and for nonlinear parametric operators trained with strongly convex losses and regularizers. Our results allow possibly infinite-dimensional inputs and outputs without independence or mixing assumptions, providing a major step towards convergence guarantees for adaptive operator learning and learning from stochastic dynamical data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.24426",
  "author_total": 1,
  "authors": [
    {
      "name": "Rafael Oliveira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/94y3pgh7ebn78.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.24426",
  "fulltext_url": null,
  "id": "94y3pgh7ebn78",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.24426",
  "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",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Machine Learning and Algorithms"
    ]
  ],
  "openalex": "W7204222070",
  "pdf_url": "https://arxiv.org/pdf/2608.24426",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/94y3pgh7ebn78.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:07Z",
      "native_id": "2608.24426",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.24426"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Sequential operator learning under dependent data",
  "title_text": "Sequential operator learning under dependent data",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:07Z",
  "url": "https://research.draconitic.com/paper/94y3pgh7ebn78",
  "venue": "arXiv",
  "versions": []
}