论文标题
基于抽样的可及性分析：一种随机集理论方法，具有对抗性抽样
Sampling-based Reachability Analysis: A Random Set Theory Approach with Adversarial Sampling
论文作者
论文摘要
可及性分析是许多应用程序的核心，从神经网络验证到不确定系统的安全轨迹计划。但是，众所周知，这个问题具有挑战性，当前的方法往往太限制了，太慢，过于保守或近似，因此缺乏保证。在本文中，我们提出了一种简单但有效的基于采样的方法，以对任意动力学系统执行可及性分析。我们的关键小说思想包括使用随机集理论对我们的方法进行严格的解释，并证明它返回的集合可以保证会融合到真实可及的集合的凸船体。此外，我们利用最新的深度学习工作，并提出了一种新的对抗性采样方法来鲁棒化我们的算法并加速其收敛性。我们证明，我们的方法比先前的工作更快，更保守，这是对神经网络的近似可及性分析的结果，以及对高维不确定的非线性系统的稳健轨迹优化，并讨论未来的应用。
Reachability analysis is at the core of many applications, from neural network verification, to safe trajectory planning of uncertain systems. However, this problem is notoriously challenging, and current approaches tend to be either too restrictive, too slow, too conservative, or approximate and therefore lack guarantees. In this paper, we propose a simple yet effective sampling-based approach to perform reachability analysis for arbitrary dynamical systems. Our key novel idea consists of using random set theory to give a rigorous interpretation of our method, and prove that it returns sets which are guaranteed to converge to the convex hull of the true reachable sets. Additionally, we leverage recent work on robust deep learning and propose a new adversarial sampling approach to robustify our algorithm and accelerate its convergence. We demonstrate that our method is faster and less conservative than prior work, present results for approximate reachability analysis of neural networks and robust trajectory optimization of high-dimensional uncertain nonlinear systems, and discuss future applications.
