# Differentiable MPC for End-to-end Planning and Control

arXiv: https://arxiv.org/abs/1810.13400 · HTML: https://mlsanity.com/paper/1810.13400/

## Key facts

- Cited by 189 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2018.

## Built on by (most cited first, 30 of 189)

- [VoxPoser: Composable 3D Value Maps for Robotic Manipulation with Language Models](https://mlsanity.com/paper/2307.05973/) (2023)
- [Affordances from Human Videos as a Versatile Representation for Robotics](https://mlsanity.com/paper/2304.08488/) (2023)
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- [SafeDiffuser: Safe Planning with Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.00148/) (2023)
- [Differentiable Integrated Motion Prediction and Planning with Learnable Cost Function for Autonomous Driving](https://mlsanity.com/paper/2207.10422/) (2022)
- [On the Importance of Hyperparameter Optimization for Model-based Reinforcement Learning](https://mlsanity.com/paper/2102.13651/) (2021)
- [LyaNet: A Lyapunov Framework for Training Neural ODEs](https://mlsanity.com/paper/2202.02526/) (2022)
- [Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems](https://mlsanity.com/paper/2103.04490/) (2021)
- [DiffStack: A Differentiable and Modular Control Stack for Autonomous Vehicles](https://mlsanity.com/paper/2212.06437/) (2022)
- [Mismatched No More: Joint Model-Policy Optimization for Model-Based RL](https://mlsanity.com/paper/2110.02758/) (2021)
- [Control-Oriented Model-Based Reinforcement Learning with Implicit Differentiation](https://mlsanity.com/paper/2106.03273/) (2021)
- [From Machine Learning to Robotics: Challenges and Opportunities for Embodied Intelligence](https://mlsanity.com/paper/2110.15245/) (2021)
- [Differentiable SLAM-net: Learning Particle SLAM for Visual Navigation](https://mlsanity.com/paper/2105.07593/) (2021)
- [Pylot: A Modular Platform for Exploring Latency-Accuracy Tradeoffs in Autonomous Vehicles](https://mlsanity.com/paper/2104.07830/) (2021)
- [INVIGORATE: Interactive Visual Grounding and Grasping in Clutter](https://mlsanity.com/paper/2108.11092/) (2021)
- [RAYEN: Imposition of Hard Convex Constraints on Neural Networks](https://mlsanity.com/paper/2307.08336/) (2023)
- [Learning Model Predictive Controllers with Real-Time Attention for Real-World Navigation](https://mlsanity.com/paper/2209.10780/) (2022)
- [Model Predictive Actor-Critic: Accelerating Robot Skill Acquisition with Deep Reinforcement Learning](https://mlsanity.com/paper/2103.13842/) (2021)
- [Simplifying Model-based RL: Learning Representations, Latent-space Models, and Policies with One Objective](https://mlsanity.com/paper/2209.08466/) (2022)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Safe Pontryagin Differentiable Programming](https://mlsanity.com/paper/2105.14937/) (2021)
- [Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classification](https://mlsanity.com/paper/2502.02133/) (2025)
- [Differentiable Spatial Planning using Transformers](https://mlsanity.com/paper/2112.01010/) (2021)
- [Learn-to-Race: A Multimodal Control Environment for Autonomous Racing](https://mlsanity.com/paper/2103.11575/) (2021)
- [Learning Modular Robot Control Policies](https://mlsanity.com/paper/2105.10049/) (2021)
- [Neural Algorithmic Reasoners are Implicit Planners](https://mlsanity.com/paper/2110.05442/) (2021)
- [Robust Implicit Networks via Non-Euclidean Contractions](https://mlsanity.com/paper/2106.03194/) (2021)
- [Policy Search for Model Predictive Control with Application to Agile Drone Flight](https://mlsanity.com/paper/2112.03850/) (2021)
- [Efficient differentiable quadratic programming layers: an ADMM approach](https://mlsanity.com/paper/2112.07464/) (2021)
- [Leaving the Nest: Going Beyond Local Loss Functions for Predict-Then-Optimize](https://mlsanity.com/paper/2305.16830/) (2023)

## Abstract (arXiv)

We present foundations for using Model Predictive Control (MPC) as a differentiable policy class for reinforcement learning in continuous state and action spaces. This provides one way of leveraging and combining the advantages of model-free and model-based approaches. Specifically, we differentiate through MPC by using the KKT conditions of the convex approximation at a fixed point of the controller. Using this strategy, we are able to learn the cost and dynamics of a controller via end-to-end learning. Our experiments focus on imitation learning in the pendulum and cartpole domains, where we learn the cost and dynamics terms of an MPC policy class. We show that our MPC policies are significantly more data-efficient than a generic neural network and that our method is superior to traditional system identification in a setting where the expert is unrealizable.