{
  "abstract": "Quadratic programs (QPs) are fundamental building blocks of many robotic tasks such as inverse kinematics, whole-body control, and model predictive control. Extending these methods to large-scale robot learning and control requires solving many QPs concurrently and, for end-to-end learning, differentiating through their solutions. Efficient batched optimization is therefore essential to bringing established model-based methods into GPU-based robotics pipelines. We present \\textsc{cuPIQP}, a batched and differentiable QP solver on GPUs based on a proximal interior-point method, with unified support for dense, sparse, and multistage problems. The solver exploits parallelism across independent QPs and their internal structure while preserving per-problem numerical updates and termination decisions. Benchmarks with up to 16384 QPs per batch demonstrate solve-time speedups of up to $18.8\\times$ over \\textsc{Moreau} and $4.26\\times$ over eight-core \\textsc{PIQP}. In an end-to-end learning task, \\textsc{cuPIQP} accelerates training by $4.6\\times$ over \\textsc{QPAX} and $7.8\\times$ over \\textsc{Moreau}. By reducing the computational cost, \\textsc{cuPIQP} provides efficient, reusable infrastructure for integrating model-based optimization into large-scale robot learning and control.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41021",
  "author_total": 5,
  "authors": [
    {
      "name": "Fenglong Song"
    },
    {
      "name": "Roland Schwan"
    },
    {
      "name": "Yuwen Chen"
    },
    {
      "name": "Yuning Jiang"
    },
    {
      "name": "Colin N. Jones"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6t2gk7q7fmvs7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41021",
  "fulltext_url": null,
  "id": "6t2gk7q7fmvs7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41021",
  "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.RO"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41021",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6t2gk7q7fmvs7.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41021",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41021"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "CuPIQP: A Batched and Differentiable QP Solver on GPUs for Robot Learning and Control",
  "title_text": "CuPIQP: A Batched and Differentiable QP Solver on GPUs for Robot Learning and Control",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/6t2gk7q7fmvs7",
  "venue": "arXiv",
  "versions": []
}