# How to Train Your Neural Control Barrier Function: Learning Safety Filters for Complex Input-Constrained Systems

arXiv: https://arxiv.org/abs/2310.15478 · HTML: https://mlsanity.com/paper/2310.15478/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2023.

## Built on by (most cited first, 30 of 44)

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- [Verification of Neural Control Barrier Functions with Symbolic Derivative Bounds Propagation](https://mlsanity.com/paper/2410.16281/) (2024)
- [Real-Time Out-of-Distribution Failure Prevention via Multi-Modal Reasoning](https://mlsanity.com/paper/2505.10547/) (2025)
- [How to Train Your Latent Control Barrier Function: Smooth Safety Filtering Under Hard-to-Model Constraints](https://mlsanity.com/paper/2511.18606/) (2025)
- [Discrete GCBF Proximal Policy Optimization for Multi-agent Safe Optimal Control](https://mlsanity.com/paper/2502.03640/) (2025)
- [Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU](https://mlsanity.com/paper/2604.07644/) (2026)
- [Safe Multi-Agent Reinforcement Learning with Convergence to Generalized Nash Equilibrium](https://mlsanity.com/paper/2411.15036/) (2024)
- [Learning Conservative Neural Control Barrier Functions from Offline Data](https://mlsanity.com/paper/2505.00908/) (2025)
- [V-OCBF: Learning Safety Filters from Offline Data via Value-Guided Offline Control Barrier Functions](https://mlsanity.com/paper/2512.10822/) (2025)
- [Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation](https://mlsanity.com/paper/2401.05629/) (2024)
- [Designing Control Barrier Function via Probabilistic Enumeration for Safe Reinforcement Learning Navigation](https://mlsanity.com/paper/2504.21643/) (2025)
- [Back to Base: Towards Hands-Off Learning via Safe Resets with Reach-Avoid Safety Filters](https://mlsanity.com/paper/2501.02620/) (2025)
- [ORN-CBF: Learning Observation-conditioned Residual Neural Control Barrier Functions via Hypernetworks](https://mlsanity.com/paper/2509.16614/) (2025)
- [Safe Control using Learned Safety Filters and Adaptive Conformal Inference](https://mlsanity.com/paper/2604.18482/) (2026)
- [Parallel Differentiable Reachability for Learning and Planning with Certified Neural Dynamics and Controllers](https://mlsanity.com/paper/2605.25346/) (2026)
- [Deep Reinforcement Learning for Reach-Avoid-Stay Problems](https://mlsanity.com/paper/2410.02898/) (2024)
- [Domain Adaptive Safety Filters via Deep Operator Learning](https://mlsanity.com/paper/2410.14528/) (2024)
- [Safe PDE Boundary Control with Neural Operators](https://mlsanity.com/paper/2411.15643/) (2024)
- [Safe Beyond the Horizon: Efficient Sampling-based MPC with Neural Control Barrier Functions](https://mlsanity.com/paper/2502.15006/) (2025)
- [Learning Neural Control Barrier Functions from Expert Demonstrations using Inverse Constraint Learning](https://mlsanity.com/paper/2510.21560/) (2025)
- [CN-CBF: Composite Neural Control Barrier Function for Robot Navigation in Dynamic Environments](https://mlsanity.com/paper/2603.06921/) (2026)
- [Dyna-Style Safety Augmented Reinforcement Learning: Staying Safe in the Face of Uncertainty](https://mlsanity.com/paper/2604.25508/) (2026)
- [Pareto Control Barrier Function for Inner Safe Set Maximization Under Input Constraints](https://mlsanity.com/paper/2410.04260/) (2024)
- [TRUST-UP: Trustworthy Reinforcement learning Using Safe Techniques for UAV Pursuit](https://mlsanity.com/paper/2411.17552/) (2024)
- [Extracting Forward Invariant Sets from Neural Network-Based Control Barrier Functions](https://mlsanity.com/paper/2501.15189/) (2025)
- [Distributed Risk-Sensitive Safety Filters for Uncertain Discrete-Time Systems](https://mlsanity.com/paper/2506.07347/) (2025)
- [Application-Specific Component-Aware Structured Pruning of Deep Neural Networks in Control via Soft Coefficient Optimization](https://mlsanity.com/paper/2507.14882/) (2025)
- [LEARN: Learning End-to-End Aerial Resource-Constrained Multi-Robot Navigation](https://mlsanity.com/paper/2511.17765/) (2025)

## Abstract (arXiv)

Control barrier functions (CBF) have become popular as a safety filter to guarantee the safety of nonlinear dynamical systems for arbitrary inputs. However, it is difficult to construct functions that satisfy the CBF constraints for high relative degree systems with input constraints. To address these challenges, recent work has explored learning CBFs using neural networks via neural CBF (NCBF). However, such methods face difficulties when scaling to higher dimensional systems under input constraints. In this work, we first identify challenges that NCBFs face during training. Next, to address these challenges, we propose policy neural CBF (PNCBF), a method of constructing CBFs by learning the value function of a nominal policy, and show that the value function of the maximum-over-time cost is a CBF. We demonstrate the effectiveness of our method in simulation on a variety of systems ranging from toy linear systems to an F-16 jet with a 16-dimensional state space. Finally, we validate our approach on a two-agent quadcopter system on hardware under tight input constraints.