论文标题
REACHLIPBNB：使用Lipschitz边界对神经自主系统的分支和结合方法分析
ReachLipBnB: A branch-and-bound method for reachability analysis of neural autonomous systems using Lipschitz bounds
论文作者
论文摘要
我们提出了一种新型的分支和结合方法，用于对开环和闭环设置中神经网络的可及性分析。我们的想法是首先使用凸面程序在某些感兴趣的神经网络的Lipschitz常数上计算精确的界限。然后，我们使用这些边界来获得使用Lipschitz的连续性参数的瞬时但保守的多面体近似。为了减少保守主义，我们将边界算法纳入分支策略中，以减少任意准确性内的过度透明度误差。然后，我们将方法扩展到具有神经网络控制器的控制系统的可及性分析。最后，为了尽可能准确地捕获可触及的集合的形状，我们使用样品轨迹使用主成分分析（PCA）告知可触及的集合过度透明度的指示。我们在几个开环和闭环设置中评估了所提出的方法的性能。
We propose a novel Branch-and-Bound method for reachability analysis of neural networks in both open-loop and closed-loop settings. Our idea is to first compute accurate bounds on the Lipschitz constant of the neural network in certain directions of interest offline using a convex program. We then use these bounds to obtain an instantaneous but conservative polyhedral approximation of the reachable set using Lipschitz continuity arguments. To reduce conservatism, we incorporate our bounding algorithm within a branching strategy to decrease the over-approximation error within an arbitrary accuracy. We then extend our method to reachability analysis of control systems with neural network controllers. Finally, to capture the shape of the reachable sets as accurately as possible, we use sample trajectories to inform the directions of the reachable set over-approximations using Principal Component Analysis (PCA). We evaluate the performance of the proposed method in several open-loop and closed-loop settings.
