{
  "abstract": "High-frequency control problems are often studied through time discretization, but refining the timestep $δ$ increases the discrete horizon $H=T/δ$ and can make standard finite-horizon regret guarantees deteriorate even when the physical horizon $T$ is fixed. We study episodic value-based reinforcement learning for Euler discretizations of controlled diffusions. The performance is measured as the cumulative regret over $K$ episodes relative to the optimal policy of the corresponding Euler model. Under stability and regularity conditions on value function gradients, Bellman residual derivatives, and fitted critics, we prove an $\\mathcal{O}(\\log K)$ regret bound with constants uniform in $δ$. For dynamics with drift linear in unknown parameters and unknown constant diffusion covariance, we verify localized versions of these conditions for a constrained, model-based controlled-diffusion fitted-$Q$ algorithm (CD-FQ) and obtain high-probability $\\mathcal{O}(\\log K\\log\\log K)$ regret for fixed and finite $T$, again with constants uniform in $δ$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36758",
  "author_total": 3,
  "authors": [
    {
      "name": "Jose Blanchet"
    },
    {
      "name": "Lutong Hao"
    },
    {
      "name": "Renyuan Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5yxpesjd0v53b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36758",
  "fulltext_url": null,
  "id": "5yxpesjd0v53b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36758",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Reinforcement Learning in Robotics"
    ]
  ],
  "openalex": "W7224136872",
  "pdf_url": "https://arxiv.org/pdf/2610.36758",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5yxpesjd0v53b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36758",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36758"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Frequency-Uniform Log-Regret Reinforcement Learning for Diffusions",
  "title_text": "Frequency-Uniform Log-Regret Reinforcement Learning for Diffusions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/5yxpesjd0v53b",
  "venue": "arXiv",
  "versions": []
}