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

arXiv: https://arxiv.org/abs/2501.03671 · HTML: https://mlsanity.com/paper/2501.03671/

## Key facts

- Cited by 3 papers in the map (data through 14 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.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Builds on (most cited first, 10 of 10)

- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Training robust neural networks using Lipschitz bounds](https://mlsanity.com/paper/2005.02929/) (2020)
- [Safe Reinforcement Learning Using Robust MPC](https://mlsanity.com/paper/1906.04005/) (2019)
- [Efficient representation and approximation of model predictive control laws via deep learning](https://mlsanity.com/paper/1806.10644/) (2018)
- [Learning an Approximate Model Predictive Controller with Guarantees](https://mlsanity.com/paper/1806.04167/) (2018)
- [LipBaB: Computing exact Lipschitz constant of ReLU networks](https://mlsanity.com/paper/2105.05495/) (2021)
- [Safe and Near-Optimal Policy Learning for Model Predictive Control using Primal-Dual Neural Networks](https://mlsanity.com/paper/1906.08257/) (2019)
- [A Sensitivity-based Data Augmentation Framework for Model Predictive Control Policy Approximation](https://mlsanity.com/paper/2009.07398/) (2020)
- [Bounding the difference between model predictive control and neural networks](https://mlsanity.com/paper/2204.06486/) (2022)
- [Efficient computation of Lipschitz constants for MPC with symmetries](https://mlsanity.com/paper/2311.04580/) (2023)

## Built on by (most cited first, 3 of 3)

- [ZipMPC: Compressed Context-Dependent MPC Cost via Imitation Learning](https://mlsanity.com/paper/2507.13088/) (2025)
- [Bridging the Sim-to-real Gap: A Control Framework for Imitation Learning of Model Predictive Control](https://mlsanity.com/paper/2503.19228/) (2025)
- [Towards Safe Learning-Based Non-Linear Model Predictive Control through Recurrent Neural Network Modeling](https://mlsanity.com/paper/2603.24503/) (2026)

## 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.