# Learning Neural Control Barrier Functions from Expert Demonstrations using Inverse Constraint Learning

arXiv: https://arxiv.org/abs/2510.21560 · HTML: https://mlsanity.com/paper/2510.21560/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 33 references that are in the map.
- First posted on arXiv 24 Oct 2025.

## Builds on (most cited first, 23 of 23)

- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods](https://mlsanity.com/paper/2202.11762/) (2022)
- [Learning Control Barrier Functions from Expert Demonstrations](https://mlsanity.com/paper/2004.03315/) (2020)
- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [Robust Control Barrier-Value Functions for Safety-Critical Control](https://mlsanity.com/paper/2104.02808/) (2021)
- [Inverse Constrained Reinforcement Learning](https://mlsanity.com/paper/2011.09999/) (2020)
- [Generalizing Safety Beyond Collision-Avoidance via Latent-Space Reachability Analysis](https://mlsanity.com/paper/2502.00935/) (2025)
- [How to Train Your Neural Control Barrier Function: Learning Safety Filters for Complex Input-Constrained Systems](https://mlsanity.com/paper/2310.15478/) (2023)
- [Maximum Likelihood Constraint Inference for Inverse Reinforcement Learning](https://mlsanity.com/paper/1909.05477/) (2019)
- [Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations](https://mlsanity.com/paper/2111.09971/) (2021)
- [SABLAS: Learning Safe Control for Black-box Dynamical Systems](https://mlsanity.com/paper/2201.01918/) (2022)
- [In-Distribution Barrier Functions: Self-Supervised Policy Filters that Avoid Out-of-Distribution States](https://mlsanity.com/paper/2301.12012/) (2023)
- [Permissive Barrier Certificates for Safe Stabilization Using Sum-of-squares](https://mlsanity.com/paper/1802.08917/) (2018)
- [Refining Control Barrier Functions through Hamilton-Jacobi Reachability](https://mlsanity.com/paper/2204.12507/) (2022)
- [Learning Shared Safety Constraints from Multi-task Demonstrations](https://mlsanity.com/paper/2309.00711/) (2023)
- [Verification and Synthesis of Control Barrier Functions](https://mlsanity.com/paper/2104.14001/) (2021)
- [Learning Constraints from Locally-Optimal Demonstrations under Cost Function Uncertainty](https://mlsanity.com/paper/2001.09336/) (2020)
- [Guaranteed Safe Spacecraft Docking with Control Barrier Functions](https://mlsanity.com/paper/2109.07027/) (2021)
- [Learning Conservative Neural Control Barrier Functions from Offline Data](https://mlsanity.com/paper/2505.00908/) (2025)
- [Your Learned Constraint is Secretly a Backward Reachable Tube](https://mlsanity.com/paper/2501.15618/) (2025)
- [Estimating Control Barriers from Offline Data](https://mlsanity.com/paper/2503.10641/) (2025)
- [Learning Autonomous Vehicle Safety Concepts from Demonstrations](https://mlsanity.com/paper/2210.02761/) (2022)

## Built on by (most cited first, 1 of 1)

- [Safe Reinforcement Learning with Receding-Horizon Safety Critic and Differentiable Action Shields](https://mlsanity.com/paper/2610.20255/) (2026)

## Abstract (arXiv)

Safety is a fundamental requirement for autonomous systems operating in critical domains. Control barrier functions (CBFs) have been used to design safety filters that minimally alter nominal controls for such systems to maintain their safety. Learning neural CBFs has been proposed as a data-driven alternative for their computationally expensive optimization-based synthesis. However, it is often the case that the failure set of states that should be avoided is non-obvious or hard to specify formally, e.g., tailgating in autonomous driving, while a set of expert demonstrations that achieve the task and avoid the failure set is easier to generate. We use ICL to train a constraint function that classifies the states of the system under consideration to safe, i.e., belong to a controlled forward invariant set that is disjoint from the unspecified failure set, and unsafe ones, i.e., belong to the complement of that set. We then use that function to label a new set of simulated trajectories to train our neural CBF. We empirically evaluate our approach in four different environments, demonstrating that it outperforms existing baselines and achieves comparable performance to a neural CBF trained with the same data but annotated with ground-truth safety labels.