# Fast Risk Assessment for Autonomous Vehicles Using Learned Models of Agent Futures

arXiv: https://arxiv.org/abs/2005.13458 · HTML: https://mlsanity.com/paper/2005.13458/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2020.

## Built on by (most cited first, 9 of 9)

- [M2I: From Factored Marginal Trajectory Prediction to Interactive Prediction](https://mlsanity.com/paper/2202.11884/) (2022)
- [HYPER: Learned Hybrid Trajectory Prediction via Factored Inference and Adaptive Sampling](https://mlsanity.com/paper/2110.02344/) (2021)
- [KEMP: Keyframe-Based Hierarchical End-to-End Deep Model for Long-Term Trajectory Prediction](https://mlsanity.com/paper/2205.04624/) (2022)
- [TIP: Task-Informed Motion Prediction for Intelligent Vehicles](https://mlsanity.com/paper/2110.08750/) (2021)
- [Risk Conditioned Neural Motion Planning](https://mlsanity.com/paper/2108.01851/) (2021)
- [Fast nonlinear risk assessment for autonomous vehicles using learned conditional probabilistic models of agent futures](https://mlsanity.com/paper/2109.09975/) (2021)
- [LaPlaSS: Latent Space Planning for Stochastic Systems](https://mlsanity.com/paper/2404.07063/) (2024)
- [Uncertainty Principles in Risk-Aware Statistical Estimation](https://mlsanity.com/paper/2104.14283/) (2021)
- [Learned Risk Metric Maps for Kinodynamic Systems](https://mlsanity.com/paper/2302.14803/) (2023)

## Abstract (arXiv)

This paper presents fast non-sampling based methods to assess the risk of trajectories for autonomous vehicles when probabilistic predictions of other agents' futures are generated by deep neural networks (DNNs). The presented methods address a wide range of representations for uncertain predictions including both Gaussian and non-Gaussian mixture models for predictions of both agent positions and controls. We show that the problem of risk assessment when Gaussian mixture models (GMMs) of agent positions are learned can be solved rapidly to arbitrary levels of accuracy with existing numerical methods. To address the problem of risk assessment for non-Gaussian mixture models of agent position, we propose finding upper bounds on risk using Chebyshev's Inequality and sums-of-squares (SOS) programming; they are both of interest as the former is much faster while the latter can be arbitrarily tight. These approaches only require statistical moments of agent positions to determine upper bounds on risk. To perform risk assessment when models are learned for agent controls as opposed to positions, we develop TreeRing, an algorithm analogous to tree search over the ring of polynomials that can be used to exactly propagate moments of control distributions into position distributions through nonlinear dynamics. The presented methods are demonstrated on realistic predictions from DNNs trained on the Argoverse and CARLA datasets and are shown to be effective for rapidly assessing the probability of low probability events.