# Quantifying Safety of Learning-based Self-Driving Control Using Almost-Barrier Functions

arXiv: https://arxiv.org/abs/2207.13891 · HTML: https://mlsanity.com/paper/2207.13891/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jul 2022.

## Built on by (most cited first, 10 of 10)

- [Iterative Reachability Estimation for Safe Reinforcement Learning](https://mlsanity.com/paper/2309.13528/) (2023)
- [Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificates](https://mlsanity.com/paper/2405.14058/) (2024)
- [Hamilton-Jacobi Reachability in Reinforcement Learning: A Survey](https://mlsanity.com/paper/2407.09645/) (2024)
- [Exact Verification of ReLU Neural Control Barrier Functions](https://mlsanity.com/paper/2310.09360/) (2023)
- [SEAL: Towards Safe Autonomous Driving via Skill-Enabled Adversary Learning for Closed-Loop Scenario Generation](https://mlsanity.com/paper/2409.10320/) (2024)
- [Sequential Neural Barriers for Scalable Dynamic Obstacle Avoidance](https://mlsanity.com/paper/2307.03015/) (2023)
- [Safe and Reliable Training of Learning-Based Aerospace Controllers](https://mlsanity.com/paper/2407.07088/) (2024)
- [Physical Deep Reinforcement Learning Towards Safety Guarantee](https://mlsanity.com/paper/2303.16860/) (2023)
- [Estimating Control Barriers from Offline Data](https://mlsanity.com/paper/2503.10641/) (2025)
- [Reachability Barrier Networks: Learning Hamilton-Jacobi Solutions for Smooth and Flexible Control Barrier Functions](https://mlsanity.com/paper/2505.11755/) (2025)

## Abstract (arXiv)

Path-tracking control of self-driving vehicles can benefit from deep learning for tackling longstanding challenges such as nonlinearity and uncertainty. However, deep neural controllers lack safety guarantees, restricting their practical use. We propose a new approach of learning almost-barrier functions, which approximately characterizes the forward invariant set for the system under neural controllers, to quantitatively analyze the safety of deep neural controllers for path-tracking. We design sampling-based learning procedures for constructing candidate neural barrier functions, and certification procedures that utilize robustness analysis for neural networks to identify regions where the barrier conditions are fully satisfied. We use an adversarial training loop between learning and certification to optimize the almost-barrier functions. The learned barrier can also be used to construct online safety monitors through reachability analysis. We demonstrate effectiveness of our methods in quantifying safety of neural controllers in various simulation environments, ranging from simple kinematic models to the TORCS simulator with high-fidelity vehicle dynamics simulation.