mlsanityData to 7 Oct 2026

Imitation Learning of MPC with Neural Networks: Error Guarantees and Sparsification

arXiv 2501.03671 ↗First posted 7 Jan 2025eess.SY cs.LG cs.SYcited by 3

On the map: Offline RL and imitation learning from data → Imitation learning methods

Abstract (arXiv)

This paper presents a framework for bounding the approximation error in imitation model predictive controllers utilizing neural networks. Leveraging the Lipschitz properties of these neural networks, we derive a bound that guides dataset design to ensure the approximation error remains at chosen limits. We discuss how this method can be used to design a stable neural network controller with performance guarantees employing existing robust model predictive control approaches for data generation. Additionally, we introduce a training adjustment, which is based on the sensitivities of the optimization problem and reduces dataset density requirements based on the derived bounds. We verify that the proposed augmentation results in improvements to the network's predictive capabilities and a reduction of the Lipschitz constant. Moreover, on a simulated inverted pendulum problem, we show that the approach results in a closer match of the closed-loop behavior between the imitation and the original model predictive controller.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data. Builds on 10 of its 29 references that are in the map. First posted on arXiv 7 Jan 2025.

Builds on

10 of 29 references.

References · 10

  1. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 290
  2. 2020Training robust neural networks using Lipschitz boundscited by 98
  3. 2019Safe Reinforcement Learning Using Robust MPCcited by 72
  4. 2018Efficient representation and approximation of model predictive control laws via deep learningcited by 55
  5. 2018Learning an Approximate Model Predictive Controller with Guaranteescited by 54
  6. 2021LipBaB: Computing exact Lipschitz constant of ReLU networkscited by 16
  7. 2019Safe and Near-Optimal Policy Learning for Model Predictive Control using Primal-Dual Neural Networkscited by 13
  8. 2020A Sensitivity-based Data Augmentation Framework for Model Predictive Control Policy Approximationcited by 6
  9. 2022Bounding the difference between model predictive control and neural networkscited by 4
  10. 2023Efficient computation of Lipschitz constants for MPC with symmetriescited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 1.

3 papers.

  1. 2025ZipMPC: Compressed Context-Dependent MPC Cost via Imitation Learningcited by 2
  2. 2025Bridging the Sim-to-real Gap: A Control Framework for Imitation Learning of Model Predictive Controlcited by 0
  3. 2026Towards Safe Learning-Based Non-Linear Model Predictive Control through Recurrent Neural Network Modelingcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Improved Sample Complexity of Imitation Learning for Barrier Model Predictive Control
  2. 2023On the Sample Complexity of Imitation Learning for Smoothed Model Predictive Control
  3. 2025Statistically Consistent Approximate Model Predictive Control
  4. 2025A Model-Based Approach to Imitation Learning through Multi-Step Predictions
  5. 2022Model Predictive Control via On-Policy Imitation Learning
  6. 2023Dissipative Imitation Learning for Discrete Dynamic Output Feedback Control with Sparse Data Sets
  7. 2023Imitation Learning from Nonlinear MPC via the Exact Q-Loss and its Gauss-Newton Approximation
  8. 2023Efficient Deep Learning of Robust Policies from MPC using Imitation and Tube-Guided Data Augmentation