mlsanityData to 14 Oct 2026

Differentiable Model Predictive Control on the GPU

arXiv 2510.06179 ↗First posted 7 Oct 2025math.OC cs.LG cs.SYcited by 7

On the map: Deep reinforcement learning methods → RL for autonomous driving and traffic

Abstract (arXiv)

Differentiable model predictive control (MPC) offers a powerful framework for combining learning and control. However, its adoption has been limited by the inherently sequential nature of traditional optimization algorithms, which are challenging to parallelize on modern computing hardware like GPUs. In this work, we tackle this bottleneck by introducing a GPU-accelerated differentiable optimization tool for MPC. This solver leverages sequential quadratic programming and a custom preconditioned conjugate gradient (PCG) routine with tridiagonal preconditioning to exploit the problem's structure and enable efficient parallelization. We demonstrate substantial speedups over CPU- and GPU-based baselines, significantly improving upon state-of-the-art training times on benchmark reinforcement learning and imitation learning tasks. Finally, we showcase the method on the challenging task of reinforcement learning for driving at the limits of handling, where it enables robust drifting of a Toyota Supra through water puddles.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Placed in RL for autonomous driving and traffic, one of 15 directions in Deep reinforcement learning methods. Builds on 33 of its 44 references that are in the map. First posted on arXiv 7 Oct 2025.

Builds on

33 of 44 references.

References · 33

  1. 2017OptNet: Differentiable Optimization as a Layer in Neural Networkscited by 599
  2. 2019Differentiable Convex Optimization Layerscited by 465
  3. 2022On Neural Differential Equationscited by 268
  4. 2021Efficient and Modular Implicit Differentiationcited by 203
  5. 2018Differentiable MPC for End-to-end Planning and Controlcited by 189
  6. 2017OSQP: An Operator Splitting Solver for Quadratic Programscited by 161
  7. 2016On Differentiating Parameterized Argmin and Argmax Problems with Application to Bi-level Optimizationcited by 112
  8. 2020learn2learn: A Library for Meta-Learning Researchcited by 69
  9. 2022Theseus: A Library for Differentiable Nonlinear Optimizationcited by 65
  10. 2019Torchmeta: A Meta-Learning library for PyTorchcited by 52
  11. 2022DiffStack: A Differentiable and Modular Control Stack for Autonomous Vehiclescited by 37
  12. 2019Differentiable Gaussian Process Motion Planningcited by 28
21 more
  1. 2022TorchOpt: An Efficient Library for Differentiable Optimizationcited by 17
  2. 2019GPU Acceleration of ADMM for Large-Scale Quadratic Programmingcited by 16
  3. 2025Primal-Dual iLQR for GPU-Accelerated Learning and Control in Legged Robotscited by 8
  4. 2023MPCGPU: Real-Time Nonlinear Model Predictive Control through Preconditioned Conjugate Gradient on the GPUcited by 7
  5. 2023ReLU-QP: A GPU-Accelerated Quadratic Programming Solver for Model-Predictive Controlcited by 7
  6. 2022CALIPSO: A Differentiable Solver for Trajectory Optimization with Conic and Complementarity Constraintscited by 6
  7. 2024DiffTORI: Differentiable Trajectory Optimization for Deep Reinforcement and Imitation Learningcited by 6
  8. 2024CusADi: A GPU Parallelization Framework for Symbolic Expressions and Optimal Controlcited by 6
  9. 2025Differentiable Nonlinear Model Predictive Controlcited by 6
  10. 2021Optimizing Trajectories with Closed-Loop Dynamic SQPcited by 5
  11. 2024Fast and Certifiable Trajectory Optimizationcited by 5
  12. 2019A Differentiable Augmented Lagrangian Method for Bilevel Nonlinear Optimizationcited by 4
  13. 2024Risk-Averse Model Predictive Control for Racing in Adverse Conditionscited by 4
  14. 2024CRONOS: Enhancing Deep Learning with Scalable GPU Accelerated Convex Neural Networkscited by 4
  15. 2024CuClarabel: GPU Acceleration for a Conic Optimization Solvercited by 4
  16. 2024First, Learn What You Don't Know: Active Information Gathering for Driving at the Limits of Handlingcited by 3
  17. 2024Fast Monte Carlo Analysis for 6-DoF Powered-Descent Guidance via GPU-Accelerated Sequential Convex Programmingcited by 2
  18. 2024DeePC-Hunt: Data-enabled Predictive Control Hyperparameter Tuning via Differentiable Optimizationcited by 2
  19. 2023Symmetric Stair Preconditioning of Linear Systems for Parallel Trajectory Optimizationcited by 1
  20. 2025Differentiable-by-design Nonlinear Optimization for Model Predictive Controlcited by 1
  21. 2025Modeling and Optimization of Control Problems on GPUscited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 7.

7 papers.

  1. 2026Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPUcited by 7
  2. 2026TurboMPC: Fast, Scalable, and Differentiable Model Predictive Control on the GPUcited by 2
  3. 2026MPC-Injection: Biasing Off-Policy Locomotion RL Toward Controller-Induced Behavior Basinscited by 1
  4. 2026CA-AC-MPC: CUDA-Accelerated Actor-Critic Model Predictive Controlcited by 0
  5. 2026Merging model-based control with multi-agent reinforcement learning for multi-agent cooperative teaming strategiescited by 0
  6. 2026Stable Transformer-Actor-Critic Model Predictive Control: A Contraction Analysis Approachcited by 0
  7. 2026Adaptive Expert Guidance for Efficient On-Policy Reinforcement Learningcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Residual MPC: Blending Reinforcement Learning with GPU-Parallelized Model Predictive Control
  2. 2025ZipMPC: Compressed Context-Dependent MPC Cost via Imitation Learning
  3. 2026Bridging RL and MPC for mixed-integer optimal control with application to Formula 1 race strategies
  4. 2025Accelerating Visual-Policy Learning through Parallel Differentiable Simulation
  5. 2026Accelerating and Scaling MPC-Guided Reinforcement Learning for Humanoid Locomotion and Manipulation
  6. 2020Infinite-Horizon Differentiable Model Predictive Control
  7. 2026Optimal Control with Learned Critics under Unmodeled State Dependencies
  8. 2026Accelerating Reinforcement Learning via MPC Solver-Gradient Guidance for Weights-varying MPC