# Certifiable Reachability Learning Using a New Lipschitz Continuous Value Function

arXiv: https://arxiv.org/abs/2408.07866 · HTML: https://mlsanity.com/paper/2408.07866/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2024.

## Built on by (most cited first, 5 of 5)

- [Statistically Assuring Safety of Control Systems using Ensembles of Safety Filters and Conformal Prediction](https://mlsanity.com/paper/2511.07899/) (2025)
- [Safe Control using Learned Safety Filters and Adaptive Conformal Inference](https://mlsanity.com/paper/2604.18482/) (2026)
- [Deep Reinforcement Learning for Reach-Avoid-Stay Problems](https://mlsanity.com/paper/2410.02898/) (2024)
- [Permissive Safety Through Trusted Inference: Verifiable Belief-Space Neural Safety Filters for Assured Interactive Robotics](https://mlsanity.com/paper/2606.02562/) (2026)
- [ResSafe: Learning Safety Filtering with Residual Reinforcement Learning for Humanoids](https://mlsanity.com/paper/2609.15988/) (2026)

## Abstract (arXiv)

We propose a new reachability learning framework for high-dimensional nonlinear systems, focusing on reach-avoid problems. These problems require computing the reach-avoid set, which ensures that all its elements can safely reach a target set despite disturbances within pre-specified bounds. Our framework has two main parts: offline learning of a newly designed reachavoid value function, and post-learning certification. Compared to prior work, our new value function is Lipschitz continuous and its associated Bellman operator is a contraction mapping, both of which improve the learning performance. To ensure deterministic guarantees of our learned reach-avoid set, we introduce two efficient post-learning certification methods. Both methods can be used online for real-time local certification or offline for comprehensive certification. We validate our framework in a 12-dimensional crazyflie drone racing hardware experiment and a simulated 10-dimensional highway take-over example.