{
  "abstract": "Variational regularization techniques are dominant in the field of mathematical imaging. The expressiveness of these methods heavily depends on the adopted regularization formulation which usually involves a number of parameters which have to be fine-tuned by the user. To circumvent the heavy computational costs associated with this parameter tuning, data-driven learning strategies have turned out to be a useful strategy. Selecting parameters by learning from data gives rise to a hierarchical (bilevel) optimization problem, which is in general computationally hard to solve. Our aim in this paper is to develop a data-efficient solution strategy for the bilevel learning problem. To that end, we propose a multilevel Monte Carlo derivative-free optimization method that couples Gaussian smoothing of the upper-level objective (parameter selection) with a hierarchy of lower-level (variational regularization) solution accuracies. Being agnostic towards the specific way the lower-level problem is solved, we derive explicit oracle complexity and computational cost statements for approximately solving the entire bilevel learning problem. Our statements are parameterized by the employed lower-level solution method, thus allowing for a direct cost accounting from the variational reconstruction method to the parameter selection problem. This enables us to give a universal end-to-end complexity analysis of bilevel learning, valid for the most important optimization routines in inverse problems, rather than for a specific choice of methods.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15047",
  "author_total": 4,
  "authors": [
    {
      "name": "Neil K. Chada"
    },
    {
      "name": "Mohammad S. Salehi"
    },
    {
      "name": "Mathias Staudigl"
    },
    {
      "name": "Simon Weissmann"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e2k6e2210t060.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15047",
  "fulltext_url": null,
  "id": "e2k6e2210t060",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15047",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7221833110",
  "pdf_url": "https://arxiv.org/pdf/2610.15047",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e2k6e2210t060.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15047",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15047"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Multilevel Monte Carlo for Zeroth-Order Stochastic Bilevel Optimization with Inexact Lower Level Solves",
  "title_text": "Multilevel Monte Carlo for Zeroth-Order Stochastic Bilevel Optimization with Inexact Lower Level Solves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/e2k6e2210t060",
  "venue": "arXiv",
  "versions": []
}