{
  "abstract": "Differentiable optimal control embeds constrained optimization problems in data-driven pipelines by differentiating their optimality conditions and propagating task-loss gradients to model or objective parameters. A key observation is that forward optimization and backward sensitivity computation involve related stage-structured linear systems, making reuse of forward factorization information natural. However, direct reuse is generally invalid, because differences in linearization, barrier terms, regularization, and curvature can create a mismatch between the retained forward operator and the target operator defining the derivative. We therefore propose RapidDOC, a factorization-reuse method that leaves the target adjoint equation unchanged. The retained cache produces a candidate adjoint and, when its target residual exceeds the prescribed tolerance, serves as a fixed right preconditioner for GMRES. A cache-action error operator characterizes directional exactness, the preconditioned iteration, and the relation between target residual and outer-gradient error. An ablation on three constrained robotic OCPs shows that the proposed method achieves lower backward time than both target-system refactorization and a no-reuse iterative method, demonstrating the computational benefit of reusing the retained forward factorizations. Across open- and closed-loop parameter-learning experiments, the proposed method achieves learning performance comparable to the baselines, while yielding the lowest open-loop backward time on all three tasks and reducing total closed-loop solver-call time by 40.5-83.1% relative to the fastest competing method. Finally, deploying the learned controller on a physical vehicle reduces the median figure-eight tracking RMSE from 22.75 to 6.09 cm, demonstrating its potential for hardware deployment.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41324",
  "author_total": 4,
  "authors": [
    {
      "name": "Xiangda Zhu"
    },
    {
      "name": "Yuankun Chen"
    },
    {
      "name": "Zifei Nie"
    },
    {
      "name": "Yi Chang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cjvnbba9kj7hs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41324",
  "fulltext_url": null,
  "id": "cjvnbba9kj7hs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41324",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41324",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cjvnbba9kj7hs.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41324",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41324"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "RapidDOC: Riccati-Preconditioned Implicit Differentiation for Differentiable Optimal Control under Operator Mismatch",
  "title_text": "RapidDOC: Riccati-Preconditioned Implicit Differentiation for Differentiable Optimal Control under Operator Mismatch",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/cjvnbba9kj7hs",
  "venue": "arXiv",
  "versions": []
}