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.
翻译:在这项工作中,我们分析一个高效的基于抽样的通用可达性分析算法,这仍然是从神经网络核查到动态系统安全分析等各种应用中一个臭名昭著的挑战性问题。通过抽样输入,在真正可达集中评价其图像,并用其$\ epsilon$ padplicate convex 的外壳作为一套测算器,这一算法适用于一般问题设置,而且易于执行。我们的主要贡献是利用随机设定理论来得出无症状和有限抽样准确性保证。这一分析为算法设计提供了信息,以便获得一个极有可能达到的近距离近距离近距离近距离的近距离近距离近距离近距离近距离近距离近距离近距离近距离的近距离近距离近距离近距离近距离近距离近距离近距离近距离的近距离,提供了对最具有挑战性的洞察力,并激发了该技术的安全关键应用。在神经网络核查任务中,我们表明这一方法比先前的工作更准确、更快得多。通过我们的分析,我们还设计了一个强大的模型预测控制器,我们在硬件实验中演示。