# Safe end-to-end imitation learning for model predictive control

arXiv: https://arxiv.org/abs/1803.10231 · HTML: https://mlsanity.com/paper/1803.10231/

## Key facts

- Cited by 12 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 11 of its 25 references that are in the map.
- First posted on arXiv 27 Mar 2018.

## Placed in

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

## Builds on (most cited first, 11 of 11)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Concrete Dropout](https://mlsanity.com/paper/1705.07832/) (2017)
- [Explaining How a Deep Neural Network Trained with End-to-End Learning Steers a Car](https://mlsanity.com/paper/1704.07911/) (2017)
- [Deep Predictive Models for Collision Risk Assessment in Autonomous Driving](https://mlsanity.com/paper/1711.10453/) (2017)
- [DropoutDAgger: A Bayesian Approach to Safe Imitation Learning](https://mlsanity.com/paper/1709.06166/) (2017)
- [MPC-Inspired Neural Network Policies for Sequential Decision Making](https://mlsanity.com/paper/1802.05803/) (2018)
- [Adaptive Probabilistic Trajectory Optimization via Efficient Approximate Inference](https://mlsanity.com/paper/1608.06235/) (2016)

## Built on by (most cited first, 12 of 12)

- [A Survey of Deep RL and IL for Autonomous Driving Policy Learning](https://mlsanity.com/paper/2101.01993/) (2021)
- [On the Sample Complexity of Stability Constrained Imitation Learning](https://mlsanity.com/paper/2102.09161/) (2021)
- [Uncertainty-Aware Data Aggregation for Deep Imitation Learning](https://mlsanity.com/paper/1905.02780/) (2019)
- [PILOT: Efficient Planning by Imitation Learning and Optimisation for Safe Autonomous Driving](https://mlsanity.com/paper/2011.00509/) (2020)
- [Better-than-Demonstrator Imitation Learning via Automatically-Ranked Demonstrations](https://mlsanity.com/paper/1907.03976/) (2019)
- [Handling Sparse Rewards in Reinforcement Learning Using Model Predictive Control](https://mlsanity.com/paper/2210.01525/) (2022)
- [Get Back Here: Robust Imitation by Return-to-Distribution Planning](https://mlsanity.com/paper/2305.01400/) (2023)
- [End-to-End Imitation Learning for Optimal Asteroid Proximity Operations](https://mlsanity.com/paper/2502.01034/) (2025)
- [Distributionally Robust Imitation Learning: Layered Control Architecture for Certifiable Autonomy](https://mlsanity.com/paper/2512.17899/) (2025)
- [MPC-guided Imitation Learning of Neural Network Policies for the Artificial Pancreas](https://mlsanity.com/paper/2003.01283/) (2020)
- [Ensemble Distribution Distillation for Self-Supervised Human Activity Recognition](https://mlsanity.com/paper/2509.08225/) (2025)
- [Addressing Ambiguity in Imitation Learning through Product of Experts based Negative Feedback](https://mlsanity.com/paper/2603.26467/) (2026)

## Abstract (arXiv)

We propose the use of Bayesian networks, which provide both a mean value and an uncertainty estimate as output, to enhance the safety of learned control policies under circumstances in which a test-time input differs significantly from the training set. Our algorithm combines reinforcement learning and end-to-end imitation learning to simultaneously learn a control policy as well as a threshold over the predictive uncertainty of the learned model, with no hand-tuning required. Corrective action, such as a return of control to the model predictive controller or human expert, is taken when the uncertainty threshold is exceeded. We validate our method on fully-observable and vision-based partially-observable systems using cart-pole and autonomous driving simulations using deep convolutional Bayesian neural networks. We demonstrate that our method is robust to uncertainty resulting from varying system dynamics as well as from partial state observability.