# Reachability-Based Safety Guarantees using Efficient Initializations

arXiv: https://arxiv.org/abs/1903.07715 · HTML: https://mlsanity.com/paper/1903.07715/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Mar 2019.

## Built on by (most cited first, 9 of 9)

- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [Exploration in Deep Reinforcement Learning: From Single-Agent to Multiagent Domain](https://mlsanity.com/paper/2109.06668/) (2021)
- [Iterative Reachability Estimation for Safe Reinforcement Learning](https://mlsanity.com/paper/2309.13528/) (2023)
- [Scalable Learning of Safety Guarantees for Autonomous Systems using Hamilton-Jacobi Reachability](https://mlsanity.com/paper/2101.05916/) (2021)
- [Real-Time Out-of-Distribution Failure Prevention via Multi-Modal Reasoning](https://mlsanity.com/paper/2505.10547/) (2025)
- [Auditing Robot Learning for Safety and Compliance during Deployment](https://mlsanity.com/paper/2110.05702/) (2021)
- [Learning Maximal Safe Sets Using Hypernetworks for MPC-based Local Trajectory Planning in Unknown Environments](https://mlsanity.com/paper/2410.20267/) (2024)
- [Residual Neural Terminal Constraint for MPC-based Collision Avoidance in Dynamic Environments](https://mlsanity.com/paper/2508.03428/) (2025)
- [An Empirical Analysis of the Use of Real-Time Reachability for the Safety Assurance of Autonomous Vehicles](https://mlsanity.com/paper/2205.01419/) (2022)

## Abstract (arXiv)

Hamilton-Jacobi-Isaacs (HJI) reachability analysis is a powerful tool for analyzing the safety of autonomous systems. This analysis is computationally intensive and typically performed offline. Online, however, the autonomous system may experience changes in system dynamics, external disturbances, and/or the surrounding environment, requiring updated safety guarantees. Rather than restarting the safety analysis, we propose a method of "warm-start" reachability, which uses a user-defined initialization (typically the previously computed solution). By starting with an HJI function that is closer to the solution than the standard initialization, convergence may take fewer iterations. In this paper we prove that warm-starting will result in guaranteed conservative solutions by over-approximating the states that must be avoided to maintain safety. We additionally prove that for many common problem formulations, warm-starting will result in exact solutions.We demonstrate our method on several illustrative examples with a double integrator, and also on a more practical example with a 10D quadcopter model that experiences changes in mass and disturbances and must update its safety guarantees accordingly. We compare our approach to standard reachability and a recently proposed "discounted" reachability method, and find for our examples that warm-starting is 1.6 times faster than standard and 6.2 times faster than (untuned) discounted reachability.