{
  "abstract": "We consider the problem of finding stationary points of stochastic convex functions and related variational inequalities. For each, we show that regularized empirical risk minimization, coupled with a random tilting perturbation, obtains stationarity residual order $\\sqrt{d/n}$ for $d$-dimensional problems given $n$ observations. We present a few complementary results that show that some dimension dependence is necessary, in distinction from standard stochastic optimization and empirical risk minimization, by providing minimax lower bounds scaling as $\\sqrt{\\log d / n}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17798",
  "author_total": 3,
  "authors": [
    {
      "name": "Felipe Areces"
    },
    {
      "name": "John C. Duchi"
    },
    {
      "name": "Malo Sommers"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4wavz6tcydxdw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17798",
  "fulltext_url": null,
  "id": "4wavz6tcydxdw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17798",
  "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",
      "math.OC"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7213515285",
  "pdf_url": "https://arxiv.org/pdf/2609.17798",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4wavz6tcydxdw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.17798",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17798"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Random tilts to find stationary points in stochastic convex optimization",
  "title_text": "Random tilts to find stationary points in stochastic convex optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:10Z",
  "url": "https://research.draconitic.com/paper/4wavz6tcydxdw",
  "venue": "arXiv",
  "versions": []
}