{
  "abstract": "In this study, we show that a continuous-time risk-sensitive control problem is equivalent to a Rényi divergence minimization problem over trajectory path measures. Reformulating stochastic optimal control as probabilistic inference via Kullback-Leibler (KL) divergence minimization avoids the computational intractability of the Hamilton-Jacobi-Bellman equation. However, standard KL control is inherently risk-neutral, and recent minimax extensions remain restricted to risk-averse settings. Our equivalence result resolves this limitation by offering a unified probabilistic framework for arbitrary risk attitudes in continuous-time nonlinear systems. Based on Girsanov theorem, we explicitly map the risk sensitivity to the Rényi divergence order, deriving a noise-dependent control penalty scaled by risk preference. This formulation seamlessly modulates tail-weighting behaviors, interpolating between zero-forcing for risk-averse policies and mass-covering for risk-seeking policies. These findings bridge stochastic control and information-theoretic inference, providing a foundation for sampling-based control algorithms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07045",
  "author_total": 3,
  "authors": [
    {
      "name": "Shinji Kataoka"
    },
    {
      "name": "Kaoru Teranishi"
    },
    {
      "name": "Yasumasa Fujisaki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a4jseexfnb0w2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07045",
  "fulltext_url": null,
  "id": "a4jseexfnb0w2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07045",
  "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.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Adaptive Dynamic Programming Control"
    ]
  ],
  "openalex": "W7212024060",
  "pdf_url": "https://arxiv.org/pdf/2609.07045",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a4jseexfnb0w2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07045",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07045"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Equivalence Between Continuous-Time Risk-Sensitive Control and Rényi Divergence Minimization",
  "title_text": "Equivalence Between Continuous-Time Risk-Sensitive Control and Rényi Divergence Minimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/a4jseexfnb0w2",
  "venue": "arXiv",
  "versions": []
}