# Designing Control Barrier Function via Probabilistic Enumeration for Safe Reinforcement Learning Navigation

arXiv: https://arxiv.org/abs/2504.21643 · HTML: https://mlsanity.com/paper/2504.21643/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Safe and constrained RL, one of 15 directions in Deep reinforcement learning methods.
- Builds on 20 of its 33 references that are in the map.
- First posted on arXiv 30 Apr 2025.

## Placed in

- Deep reinforcement learning methods / [Safe and constrained RL](https://mlsanity.com/deeprl/safe-and-constrained-rl/)

## Builds on (most cited first, 20 of 20)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Responsive Safety in Reinforcement Learning by PID Lagrangian Methods](https://mlsanity.com/paper/2007.03964/) (2020)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [Safety-Gymnasium: A Unified Safe Reinforcement Learning Benchmark](https://mlsanity.com/paper/2310.12567/) (2023)
- [OmniSafe: An Infrastructure for Accelerating Safe Reinforcement Learning Research](https://mlsanity.com/paper/2305.09304/) (2023)
- [Penalized Proximal Policy Optimization for Safe Reinforcement Learning](https://mlsanity.com/paper/2205.11814/) (2022)
- [How to Train Your Neural Control Barrier Function: Learning Safety Filters for Complex Input-Constrained Systems](https://mlsanity.com/paper/2310.15478/) (2023)
- [Verifying Learning-Based Robotic Navigation Systems](https://mlsanity.com/paper/2205.13536/) (2022)
- [Safe Control Under Input Limits with Neural Control Barrier Functions](https://mlsanity.com/paper/2211.11056/) (2022)
- [The #DNN-Verification Problem: Counting Unsafe Inputs for Deep Neural Networks](https://mlsanity.com/paper/2301.07068/) (2023)
- [Enumerating Safe Regions in Deep Neural Networks with Provable Probabilistic Guarantees](https://mlsanity.com/paper/2308.09842/) (2023)
- [Verification of Neural Control Barrier Functions with Symbolic Derivative Bounds Propagation](https://mlsanity.com/paper/2410.16281/) (2024)
- [Safe Deep Reinforcement Learning by Verifying Task-Level Properties](https://mlsanity.com/paper/2302.10030/) (2023)
- [Neural Control Barrier Functions for Safe Navigation](https://mlsanity.com/paper/2407.19907/) (2024)
- [Online Safety Property Collection and Refinement for Safe Deep Reinforcement Learning in Mapless Navigation](https://mlsanity.com/paper/2302.06695/) (2023)
- [Improving Policy Optimization via varepsilon-Retrain](https://mlsanity.com/paper/2406.08315/) (2024)
- [A Dynamic Safety Shield for Safe and Efficient Reinforcement Learning of Navigation Tasks](https://mlsanity.com/paper/2412.04153/) (2024)

## Built on by (most cited first, 3 of 3)

- [Zero-Shot, Safe and Time-Efficient UAV Navigation via Potential-Based Reward Shaping, Control Lyapunov and Barrier Functions](https://mlsanity.com/paper/2605.01787/) (2026)
- [Probabilistic Verification of Recurrent Neural Networks for Single and Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2605.14758/) (2026)
- [A Survey on the Verification of Reinforcement Learning Policies](https://mlsanity.com/paper/2607.16210/) (2026)

## Abstract (arXiv)

Achieving safe autonomous navigation systems is critical for deploying robots in dynamic and uncertain real-world environments. In this paper, we propose a hierarchical control framework leveraging neural network verification techniques to design control barrier functions (CBFs) and policy correction mechanisms that ensure safe reinforcement learning navigation policies. Our approach relies on probabilistic enumeration to identify unsafe regions of operation, which are then used to construct a safe CBF-based control layer applicable to arbitrary policies. We validate our framework both in simulation and on a real robot, using a standard mobile robot benchmark and a highly dynamic aquatic environmental monitoring task. These experiments demonstrate the ability of the proposed solution to correct unsafe actions while preserving efficient navigation behavior. Our results show the promise of developing hierarchical verification-based systems to enable safe and robust navigation behaviors in complex scenarios.