# CP-NCBF: A Conformal Prediction-based Approach to Synthesize Verified Neural Control Barrier Functions

arXiv: https://arxiv.org/abs/2503.17395 · HTML: https://mlsanity.com/paper/2503.17395/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 31 references that are in the map.
- First posted on arXiv 18 Mar 2025.

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

- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functions](https://mlsanity.com/paper/2109.06697/) (2021)
- [Learning Control Barrier Functions from Expert Demonstrations](https://mlsanity.com/paper/2004.03315/) (2020)
- [Learning to Fly -- a Gym Environment with PyBullet Physics for Reinforcement Learning of Multi-agent Quadcopter Control](https://mlsanity.com/paper/2103.02142/) (2021)
- [Model-based Safe Deep Reinforcement Learning via a Constrained Proximal Policy Optimization Algorithm](https://mlsanity.com/paper/2210.07573/) (2022)
- [Formal Synthesis of Stochastic Systems via Control Barrier Certificates](https://mlsanity.com/paper/1905.04585/) (2019)
- [Exact Verification of ReLU Neural Control Barrier Functions](https://mlsanity.com/paper/2310.09360/) (2023)
- [A Physics-Informed Machine Learning Framework for Safe and Optimal Control of Autonomous Systems](https://mlsanity.com/paper/2502.11057/) (2025)
- [Learning a Formally Verified Control Barrier Function in Stochastic Environment](https://mlsanity.com/paper/2403.19332/) (2024)
- [Control Barrier Functions in Dynamic UAVs for Kinematic Obstacle Avoidance: A Collision Cone Approach](https://mlsanity.com/paper/2303.15871/) (2023)
- [Semi-Supervised Safe Visuomotor Policy Synthesis using Barrier Certificates](https://mlsanity.com/paper/2409.12616/) (2024)
- [SEEV: Synthesis with Efficient Exact Verification for ReLU Neural Barrier Functions](https://mlsanity.com/paper/2410.20326/) (2024)

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

- [Safety Certification in the Latent space using Control Barrier Functions and World Models](https://mlsanity.com/paper/2507.13871/) (2025)
- [Neural Control Barrier Functions from Physics Informed Neural Networks](https://mlsanity.com/paper/2504.11045/) (2025)
- [MAD-PINN: A Decentralized Physics-Informed Machine Learning Framework for Safe and Optimal Multi-Agent Control](https://mlsanity.com/paper/2509.23960/) (2025)
- [CrossSafe: Towards Cross-Embodiment Latent Safety Filters](https://mlsanity.com/paper/2609.28984/) (2026)

## Abstract (arXiv)

Control Barrier Functions (CBFs) are a practical approach for designing safety-critical controllers, but constructing them for arbitrary nonlinear dynamical systems remains a challenge. Recent efforts have explored learning-based methods, such as neural CBFs (NCBFs), to address this issue. However, ensuring the validity of NCBFs is difficult due to potential learning errors. In this letter, we propose a novel framework that leverages split-conformal prediction to generate formally verified neural CBFs with probabilistic guarantees based on a user-defined error rate, referred to as CP-NCBF. Unlike existing methods that impose Lipschitz constraints on neural CBF-leading to scalability limitations and overly conservative safe sets--our approach is sample-efficient, scalable, and results in less restrictive safety regions. We validate our framework through case studies on obstacle avoidance in autonomous driving and geo-fencing of aerial vehicles, demonstrating its ability to generate larger and less conservative safe sets compared to conventional techniques.