mlsanityData to 14 Oct 2026

Differentiable MPC for End-to-end Planning and Control

arXiv 1810.13400 ↗First posted 31 Oct 2018cs.LG cs.AI math.OCcited by 189

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Cited by 23 in Deep reinforcement learning methods, but placed by its own abstract, which didn’t fit.

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.

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

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Citing papers per year: 2020: 1; 2021: 35; 2022: 46; 2023: 30; 2024: 27; 2025: 25; 2026: 25.

189 papers.

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  1. 2023VoxPoser: Composable 3D Value Maps for Robotic Manipulation with Language Modelscited by 750
  2. 2023Affordances from Human Videos as a Versatile Representation for Roboticscited by 226
  3. 2022Tutorial on amortized optimizationcited by 83
  4. 2023SafeDiffuser: Safe Planning with Diffusion Probabilistic Modelscited by 75
  5. 2022Differentiable Integrated Motion Prediction and Planning with Learnable Cost Function for Autonomous Drivingcited by 73
  6. 2021On the Importance of Hyperparameter Optimization for Model-based Reinforcement Learningcited by 59
  7. 2022LyaNet: A Lyapunov Framework for Training Neural ODEscited by 44
  8. 2021Adaptive-Control-Oriented Meta-Learning for Nonlinear Systemscited by 39
  9. 2022DiffStack: A Differentiable and Modular Control Stack for Autonomous Vehiclescited by 37
  10. 2021Mismatched No More: Joint Model-Policy Optimization for Model-Based RLcited by 36
  11. 2021Control-Oriented Model-Based Reinforcement Learning with Implicit Differentiationcited by 35
  12. 2021From Machine Learning to Robotics: Challenges and Opportunities for Embodied Intelligencecited by 35
38 more
  1. 2021Differentiable SLAM-net: Learning Particle SLAM for Visual Navigationcited by 34
  2. 2021Pylot: A Modular Platform for Exploring Latency-Accuracy Tradeoffs in Autonomous Vehiclescited by 33
  3. 2021INVIGORATE: Interactive Visual Grounding and Grasping in Cluttercited by 32
  4. 2023RAYEN: Imposition of Hard Convex Constraints on Neural Networkscited by 30
  5. 2022Learning Model Predictive Controllers with Real-Time Attention for Real-World Navigationcited by 29
  6. 2021Model Predictive Actor-Critic: Accelerating Robot Skill Acquisition with Deep Reinforcement Learningcited by 28
  7. 2022Simplifying Model-based RL: Learning Representations, Latent-space Models, and Policies with One Objectivecited by 28
  8. 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
  9. 2021Safe Pontryagin Differentiable Programmingcited by 26
  10. 2025Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classificationcited by 26
  11. 2021Differentiable Spatial Planning using Transformerscited by 25
  12. 2021Learn-to-Race: A Multimodal Control Environment for Autonomous Racingcited by 23
  13. 2021Learning Modular Robot Control Policiescited by 22
  14. 2021Neural Algorithmic Reasoners are Implicit Plannerscited by 21
  15. 2021Robust Implicit Networks via Non-Euclidean Contractionscited by 20
  16. 2021Policy Search for Model Predictive Control with Application to Agile Drone Flightcited by 20
  17. 2021Efficient differentiable quadratic programming layers: an ADMM approachcited by 19
  18. 2023Leaving the Nest: Going Beyond Local Loss Functions for Predict-Then-Optimizecited by 18
  19. 2022Control-oriented meta-learningcited by 17
  20. 2022Distributionally Robust End-to-End Portfolio Constructioncited by 17
  21. 2024Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomycited by 16
  22. 2021Joint inference and input optimization in equilibrium networkscited by 15
  23. 2023Targeted Reduction of Causal Modelscited by 15
  24. 2023Learning for CasADi: Data-driven Models in Numerical Optimizationcited by 15
  25. 2022When to Update Your Model: Constrained Model-based Reinforcement Learningcited by 14
  26. 2022Learning Robotic Navigation from Experience: Principles, Methods, and Recent Resultscited by 13
  27. 2024Residual Policy Learning for Perceptive Quadruped Control Using Differentiable Simulationcited by 13
  28. 2022Decision-Focused Learning without Differentiable Optimization: Learning Locally Optimized Decision Lossescited by 12
  29. 2023CCIL: Context-conditioned imitation learning for urban drivingcited by 12
  30. 2021Deep Learning Explicit Differentiable Predictive Control Laws for Buildingscited by 11
  31. 2022On the Forward Invariance of Neural ODEscited by 11
  32. 2022Learning to Optimize in Model Predictive Controlcited by 11
  33. 2023TaskMet: Task-Driven Metric Learning for Model Learningcited by 11
  34. 2024NeuPAN: Direct Point Robot Navigation with End-to-End Model-based Learningcited by 11
  35. 2021Neural Fixed-Point Acceleration for Convex Optimizationcited by 10
  36. 2022Differentiable Control Barrier Functions for Vision-based End-to-End Autonomous Drivingcited by 10
  37. 2022Learning Sampling Distributions for Model Predictive Controlcited by 10
  38. 2024Differentiation Through Black-Box Quadratic Programming Solverscited by 10

50 most cited of 189 All 189 (JSON)

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  1. 2024Faster Model Predictive Control via Self-Supervised Initialization Learning
  2. 2020Learning Constrained Adaptive Differentiable Predictive Control Policies With Guarantees
  3. 2020Infinite-Horizon Differentiable Model Predictive Control
  4. 2026Optimal Control with Learned Critics under Unmodeled State Dependencies
  5. 2022Model Predictive Control via On-Policy Imitation Learning
  6. 2024Diffusion Model Predictive Control
  7. 2026Dream-MPC: Gradient-Based Model Predictive Control with Latent Imagination
  8. 2025Bootstrapped Model Predictive Control