{
  "abstract": "We study the convergence of the vanilla stochastic policy gradient method applied to the linear quadratic regulator (LQR) problem. The method is cheap in the following sense: (1) at each iteration only $\\tilde{O}(1)$ interactions with the environment are needed, therefore allowing frequent policy improvement steps, and (2) to ensure stability throughout and convergence to an $ε$-optimal policy with probability $1-δ$, only $O(\\mathtt{Polylog}(1/δ)/ε)$ interactions are needed. To the best of our knowledge, this appears to be the first time that a stochastic model-free policy optimization method for LQR converges with high probability with $\\tilde{O}(1)$ per-iteration computation and polylogarithmic dependence on the confidence level. The convergence analysis presented here is agnostic to LQR specifics and hence could be potentially generalized to a broader class of problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19712",
  "author_total": 2,
  "authors": [
    {
      "name": "Yan Li"
    },
    {
      "name": "Chengze Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bb3fst2eygqbd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19712",
  "fulltext_url": null,
  "id": "bb3fst2eygqbd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19712",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.19712",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bb3fst2eygqbd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19712",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19712"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "(Cheap) Stochastic Policy Gradient Converges with High Probability for Linear Quadratic Regulator",
  "title_text": "(Cheap) Stochastic Policy Gradient Converges with High Probability for Linear Quadratic Regulator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/bb3fst2eygqbd",
  "venue": "arXiv",
  "versions": []
}