CuPIQP: A Batched and Differentiable QP Solver on GPUs for Robot Learning and Control
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× over \textsc{Moreau} and 4.26× over eight-core \textsc{PIQP}. In an end-to-end learning task, \textsc{cuPIQP} accelerates training by 4.6× over \textsc{QPAX} and 7.8× 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.
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BibTeX
@misc{song2026cupiqp,
title = {{CuPIQP: A Batched and Differentiable QP Solver on GPUs for Robot Learning and Control}},
author = {Fenglong Song and Roland Schwan and Yuwen Chen and Yuning Jiang and Colin N. Jones},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41021},
eprint = {2610.41021},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41021},
}
RIS
TY - UNPB
TI - CuPIQP: A Batched and Differentiable QP Solver on GPUs for Robot Learning and Control
AU - Fenglong Song
AU - Roland Schwan
AU - Yuwen Chen
AU - Yuning Jiang
AU - Colin N. Jones
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.41021
UR - https://arxiv.org/abs/2610.41021
AB - 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× over \textsc{Moreau} and 4.26× over eight-core \textsc{PIQP}. In an end-to-end learning task, \textsc{cuPIQP} accelerates training by 4.6× over \textsc{QPAX} and 7.8× 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.
ER -