# Adversarial Mixture Density Networks: Learning to Drive Safely from Collision Data

arXiv: https://arxiv.org/abs/2107.04485 · HTML: https://mlsanity.com/paper/2107.04485/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Imitation and offline RL for driving, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 17 of its 37 references that are in the map.
- First posted on arXiv 9 Jul 2021.

## Placed in

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

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Deep Reinforcement Learning that Matters](https://mlsanity.com/paper/1709.06560/) (2017)
- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [ChauffeurNet: Learning to Drive by Imitating the Best and Synthesizing the Worst](https://mlsanity.com/paper/1812.03079/) (2018)
- [Causal Confusion in Imitation Learning](https://mlsanity.com/paper/1905.11979/) (2019)
- [Deep Reinforcement Learning framework for Autonomous Driving](https://mlsanity.com/paper/1704.02532/) (2017)
- [A Survey of Deep Learning Applications to Autonomous Vehicle Control](https://mlsanity.com/paper/1912.10773/) (2019)
- [Overcoming Limitations of Mixture Density Networks: A Sampling and Fitting Framework for Multimodal Future Prediction](https://mlsanity.com/paper/1906.03631/) (2019)
- [On Offline Evaluation of Vision-based Driving Models](https://mlsanity.com/paper/1809.04843/) (2018)
- [Deep Object-Centric Policies for Autonomous Driving](https://mlsanity.com/paper/1811.05432/) (2018)
- [Probabilistic Prediction of Vehicle Semantic Intention and Motion](https://mlsanity.com/paper/1804.03629/) (2018)
- [End-to-End Learning of Driving Models with Surround-View Cameras and Route Planners](https://mlsanity.com/paper/1803.10158/) (2018)
- [Uncertainty-Aware Learning from Demonstration using Mixture Density Networks with Sampling-Free Variance Modeling](https://mlsanity.com/paper/1709.02249/) (2017)
- [Training Adversarial Agents to Exploit Weaknesses in Deep Control Policies](https://mlsanity.com/paper/2002.12078/) (2020)
- [Autonomous Braking System via Deep Reinforcement Learning](https://mlsanity.com/paper/1702.02302/) (2017)
- [Learning Probabilistic Multi-Modal Actor Models for Vision-Based Robotic Grasping](https://mlsanity.com/paper/1904.07319/) (2019)

## Built on by (most cited first, 4 of 4)

- [MoVEInt: Mixture of Variational Experts for Learning Human-Robot Interactions from Demonstrations](https://mlsanity.com/paper/2407.07636/) (2024)
- [Symbolic Imitation Learning: From Black-Box to Explainable Driving Policies](https://mlsanity.com/paper/2309.16025/) (2023)
- [Offline Reinforcement Learning using Human-Aligned Reward Labeling for Autonomous Emergency Braking in Occluded Pedestrian Crossing](https://mlsanity.com/paper/2504.08704/) (2025)
- [Human-Like Autonomous Driving on Dense Traffic](https://mlsanity.com/paper/2310.02477/) (2023)

## Abstract (arXiv)

Imitation learning has been widely used to learn control policies for autonomous driving based on pre-recorded data. However, imitation learning based policies have been shown to be susceptible to compounding errors when encountering states outside of the training distribution. Further, these agents have been demonstrated to be easily exploitable by adversarial road users aiming to create collisions. To overcome these shortcomings, we introduce Adversarial Mixture Density Networks (AMDN), which learns two distributions from separate datasets. The first is a distribution of safe actions learned from a dataset of naturalistic human driving. The second is a distribution representing unsafe actions likely to lead to collision, learned from a dataset of collisions. During training, we leverage these two distributions to provide an additional loss based on the similarity of the two distributions. By penalising the safe action distribution based on its similarity to the unsafe action distribution when training on the collision dataset, a more robust and safe control policy is obtained. We demonstrate the proposed AMDN approach in a vehicle following use-case, and evaluate under naturalistic and adversarial testing environments. We show that despite its simplicity, AMDN provides significant benefits for the safety of the learned control policy, when compared to pure imitation learning or standard mixture density network approaches.