A Simple and Efficient Sampling-based Algorithm for General Reachability Analysis
This work addresses reachability analysis, a critical problem for safety verification in domains like neural networks and dynamical systems, though it appears incremental as it builds on sampling-based methods with new theoretical guarantees.
The authors tackled the challenging problem of general reachability analysis by proposing a simple sampling-based algorithm that uses input sampling and convex hull estimation. They demonstrated that this approach is more accurate and significantly faster than prior methods on a neural network verification task, with hardware experiments showing practical application in robust model predictive control.
In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of dynamical systems. By sampling inputs, evaluating their images in the true reachable set, and taking their $ε$-padded convex hull as a set estimator, this algorithm applies to general problem settings and is simple to implement. Our main contribution is the derivation of asymptotic and finite-sample accuracy guarantees using random set theory. This analysis informs algorithmic design to obtain an $ε$-close reachable set approximation with high probability, provides insights into which reachability problems are most challenging, and motivates safety-critical applications of the technique. On a neural network verification task, we show that this approach is more accurate and significantly faster than prior work. Informed by our analysis, we also design a robust model predictive controller that we demonstrate in hardware experiments.