# A Classification-based Approach for Approximate Reachability

arXiv: https://arxiv.org/abs/1803.03237 · HTML: https://mlsanity.com/paper/1803.03237/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2018.

## Built on by (most cited first, 10 of 10)

- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [Safety and Liveness Guarantees through Reach-Avoid Reinforcement Learning](https://mlsanity.com/paper/2112.12288/) (2021)
- [Verification of Neural Reachable Tubes via Scenario Optimization and Conformal Prediction](https://mlsanity.com/paper/2312.08604/) (2023)
- [Generating Formal Safety Assurances for High-Dimensional Reachability](https://mlsanity.com/paper/2209.12336/) (2022)
- [Human-AI Safety: A Descendant of Generative AI and Control Systems Safety](https://mlsanity.com/paper/2405.09794/) (2024)
- [Verifiable Safety Q-Filters via Hamilton-Jacobi Reachability and Multiplicative Q-Networks](https://mlsanity.com/paper/2506.15693/) (2025)
- [Physics-informed RL for Maximal Safety Probability Estimation](https://mlsanity.com/paper/2403.16391/) (2024)
- [The Feasibility Theory of Constrained Reinforcement Learning: A Tutorial Study](https://mlsanity.com/paper/2404.10064/) (2024)
- [Verified Compositional Neuro-Symbolic Control for Stochastic Systems with Temporal Logic Tasks](https://mlsanity.com/paper/2311.10863/) (2023)
- [Efficient Safety Verification of Autonomous Vehicles with Neural Network Operator](https://mlsanity.com/paper/2512.04557/) (2025)

## Abstract (arXiv)

Hamilton-Jacobi (HJ) reachability analysis has been developed over the past decades into a widely-applicable tool for determining goal satisfaction and safety verification in nonlinear systems. While HJ reachability can be formulated very generally, computational complexity can be a serious impediment for many systems of practical interest. Much prior work has been devoted to computing approximate solutions to large reachability problems, yet many of these methods may only apply to very restrictive problem classes, do not generate controllers, and/or can be extremely conservative. In this paper, we present a new method for approximating the optimal controller of the HJ reachability problem for control-affine systems. While also a specific problem class, many dynamical systems of interest are, or can be well approximated, by control-affine models. We explicitly avoid storing a representation of the reachability value function, and instead learn a controller as a sequence of simple binary classifiers. We compare our approach to existing grid-based methodologies in HJ reachability and demonstrate its utility on several examples, including a physical quadrotor navigation task.