# Limits of Probabilistic Safety Guarantees when Considering Human Uncertainty

arXiv: https://arxiv.org/abs/2103.03388 · HTML: https://mlsanity.com/paper/2103.03388/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2021.

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

- [RAP: Risk-Aware Prediction for Robust Planning](https://mlsanity.com/paper/2210.01368/) (2022)
- [Trajectory Optimization of Chance-Constrained Nonlinear Stochastic Systems for Motion Planning Under Uncertainty](https://mlsanity.com/paper/2106.02801/) (2021)
- [Distance-Aware Error for Spline Networks: A Bottom-Up Approach to Uncertainty](https://mlsanity.com/paper/2501.04757/) (2025)
- [Worst-Case Distance-Aware Error Bounds for Neural Networks](https://mlsanity.com/paper/2510.22021/) (2025)

## Abstract (arXiv)

When autonomous robots interact with humans, such as during autonomous driving, explicit safety guarantees are crucial in order to avoid potentially life-threatening accidents. Many data-driven methods have explored learning probabilistic bounds over human agents' trajectories (i.e. confidence tubes that contain trajectories with probability δ), which can then be used to guarantee safety with probability 1-δ. However, almost all existing works consider δ ≥ 0.001. The purpose of this paper is to argue that (1) in safety-critical applications, it is necessary to provide safety guarantees with δ < 10-8, and (2) current learning-based methods are ill-equipped to compute accurate confidence bounds at such low δ. Using human driving data (from the highD dataset), as well as synthetically generated data, we show that current uncertainty models use inaccurate distributional assumptions to describe human behavior and/or require infeasible amounts of data to accurately learn confidence bounds for δ ≤ 10-8. These two issues result in unreliable confidence bounds, which can have dangerous implications if deployed on safety-critical systems.