# Differentiable Model Predictive Control on the GPU

arXiv: https://arxiv.org/abs/2510.06179 · HTML: https://mlsanity.com/paper/2510.06179/

## 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.

## Placed in

- Deep reinforcement learning methods / [RL for autonomous driving and traffic](https://mlsanity.com/deeprl/rl-for-autonomous-driving-and-traffic/)

## Builds on (most cited first, 30 of 33)

- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [On Differentiating Parameterized Argmin and Argmax Problems with Application to Bi-level Optimization](https://mlsanity.com/paper/1607.05447/) (2016)
- [learn2learn: A Library for Meta-Learning Research](https://mlsanity.com/paper/2008.12284/) (2020)
- [Theseus: A Library for Differentiable Nonlinear Optimization](https://mlsanity.com/paper/2207.09442/) (2022)
- [Torchmeta: A Meta-Learning library for PyTorch](https://mlsanity.com/paper/1909.06576/) (2019)
- [DiffStack: A Differentiable and Modular Control Stack for Autonomous Vehicles](https://mlsanity.com/paper/2212.06437/) (2022)
- [Differentiable Gaussian Process Motion Planning](https://mlsanity.com/paper/1907.09591/) (2019)
- [TorchOpt: An Efficient Library for Differentiable Optimization](https://mlsanity.com/paper/2211.06934/) (2022)
- [GPU Acceleration of ADMM for Large-Scale Quadratic Programming](https://mlsanity.com/paper/1912.04263/) (2019)
- [Primal-Dual iLQR for GPU-Accelerated Learning and Control in Legged Robots](https://mlsanity.com/paper/2506.07823/) (2025)
- [MPCGPU: Real-Time Nonlinear Model Predictive Control through Preconditioned Conjugate Gradient on the GPU](https://mlsanity.com/paper/2309.08079/) (2023)
- [ReLU-QP: A GPU-Accelerated Quadratic Programming Solver for Model-Predictive Control](https://mlsanity.com/paper/2311.18056/) (2023)
- [CALIPSO: A Differentiable Solver for Trajectory Optimization with Conic and Complementarity Constraints](https://mlsanity.com/paper/2205.09255/) (2022)
- [DiffTORI: Differentiable Trajectory Optimization for Deep Reinforcement and Imitation Learning](https://mlsanity.com/paper/2402.05421/) (2024)
- [CusADi: A GPU Parallelization Framework for Symbolic Expressions and Optimal Control](https://mlsanity.com/paper/2408.09662/) (2024)
- [Differentiable Nonlinear Model Predictive Control](https://mlsanity.com/paper/2505.01353/) (2025)
- [Optimizing Trajectories with Closed-Loop Dynamic SQP](https://mlsanity.com/paper/2109.07081/) (2021)
- [Fast and Certifiable Trajectory Optimization](https://mlsanity.com/paper/2406.05846/) (2024)
- [A Differentiable Augmented Lagrangian Method for Bilevel Nonlinear Optimization](https://mlsanity.com/paper/1902.03319/) (2019)
- [Risk-Averse Model Predictive Control for Racing in Adverse Conditions](https://mlsanity.com/paper/2410.17183/) (2024)
- [CRONOS: Enhancing Deep Learning with Scalable GPU Accelerated Convex Neural Networks](https://mlsanity.com/paper/2411.01088/) (2024)
- [CuClarabel: GPU Acceleration for a Conic Optimization Solver](https://mlsanity.com/paper/2412.19027/) (2024)
- [First, Learn What You Don't Know: Active Information Gathering for Driving at the Limits of Handling](https://mlsanity.com/paper/2411.00107/) (2024)
- [Fast Monte Carlo Analysis for 6-DoF Powered-Descent Guidance via GPU-Accelerated Sequential Convex Programming](https://mlsanity.com/paper/2404.18034/) (2024)
- [DeePC-Hunt: Data-enabled Predictive Control Hyperparameter Tuning via Differentiable Optimization](https://mlsanity.com/paper/2412.06481/) (2024)

## Built on by (most cited first, 7 of 7)

- [Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU](https://mlsanity.com/paper/2604.07644/) (2026)
- [TurboMPC: Fast, Scalable, and Differentiable Model Predictive Control on the GPU](https://mlsanity.com/paper/2606.24039/) (2026)
- [MPC-Injection: Biasing Off-Policy Locomotion RL Toward Controller-Induced Behavior Basins](https://mlsanity.com/paper/2606.26392/) (2026)
- [CA-AC-MPC: CUDA-Accelerated Actor-Critic Model Predictive Control](https://mlsanity.com/paper/2605.29155/) (2026)
- [Merging model-based control with multi-agent reinforcement learning for multi-agent cooperative teaming strategies](https://mlsanity.com/paper/2606.06011/) (2026)
- [Stable Transformer-Actor-Critic Model Predictive Control: A Contraction Analysis Approach](https://mlsanity.com/paper/2606.20197/) (2026)
- [Adaptive Expert Guidance for Efficient On-Policy Reinforcement Learning](https://mlsanity.com/paper/2610.06019/) (2026)

## 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.