A Simple and Efficient Sampling-based Algorithm for General Reachability Analysis

• URL: http://arxiv.org/abs/2112.05745v1
• Date: Fri, 10 Dec 2021 18:56:16 GMT
• Title: A Simple and Efficient Sampling-based Algorithm for General Reachability Analysis
• Authors: Thomas Lew, Lucas Janson, Riccardo Bonalli, Marco Pavone
• Abstract summary: General-purpose reachability analysis 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 $epsilon$-padded convex hull as a set estimator, this algorithm applies to general problem settings and is simple to implement. This analysis informs algorithmic design to obtain an $epsilon$-close reachable set approximation with high probability. On a neural network verification task, we show that this approach is more accurate and significantly faster than prior work.
• Score: 32.488975902387395
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\epsilon$-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 $\epsilon$-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.

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