{
  "abstract": "We study continuous-time full-order dynamic output-feedback $H_\\infty$ policy search, a nonconvex and nonsmooth problem. Direct policy search is a central paradigm in reinforcement learning and continuous control, but rigorous guarantees remain scarce in robust output-feedback settings. The $H_\\infty$ problem is a canonical benchmark because it captures disturbance attenuation and robustness while exposing the hard nonsmooth geometry of policy-space optimization. We prove that on the exact identity-gauge slice of the extended convex lift, $\\varepsilon$-stationarity yields $O(\\varepsilon)$-suboptimality on compact exact slices, which in turn yields convergence-rate guarantees for nonsmooth policy-search methods. This result addresses the finite-time optimality-gap question raised by Guo and Hu [2022] in the more general dynamic output-feedback $H_\\infty$ policy-search setting. We further use the established value equivalence supplied by extended convex lifting to formulate a nonstrict-feasibility bisection method with one final strict-feasibility recovery step, yielding an explicit $\\varepsilon$-optimal stabilizing controller. These results provide a quantitative and algorithmic strengthening of prior qualitative optimality theory for nonsmooth $H_\\infty$ policy search.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06197",
  "author_total": 2,
  "authors": [
    {
      "name": "Ashkan Soleymani"
    },
    {
      "name": "Patrick Jaillet"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8pasfvxrzfkj7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06197",
  "fulltext_url": null,
  "id": "8pasfvxrzfkj7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06197",
  "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.LG"
    ],
    [
      "arxiv",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Adaptive Dynamic Programming Control"
    ]
  ],
  "openalex": "W7212028532",
  "pdf_url": "https://arxiv.org/pdf/2609.06197",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8pasfvxrzfkj7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.06197",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06197"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Algorithmic Optimality Guarantees for Nonsmooth $H_\\infty$ Output-Feedback Policy Search",
  "title_text": "Algorithmic Optimality Guarantees for Nonsmooth H_∞ Output-Feedback Policy Search",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/8pasfvxrzfkj7",
  "venue": "arXiv",
  "versions": []
}