论文标题
SREACHTOOLS内核模块：使用Hilbert空间嵌入分布的数据驱动随机可达性
SReachTools Kernel Module: Data-Driven Stochastic Reachability Using Hilbert Space Embeddings of Distributions
论文作者
论文摘要
我们提出了用于执行数据驱动的随机可及性的算法，作为一种开源随机可及性工具箱SREACHTOOLS的补充。我们的方法利用一类称为分布的内核嵌入的机器学习技术，以近似于各种随机可及性问题的安全概率。通过将系统状态的概率分布表示为复制的内核希尔伯特空间中的元素，我们可以通过简单的正规化最小二乘问题来学习“最佳拟合”分布，然后将随机可达性安全性概率作为简单的线性操作计算。该技术接收有限的样品边界，并且在概率上具有已知收敛性。我们将这些方法作为SREACHTOOLS的一部分实施，并在双积分系统，在百万个维重复的平面四面体系统上演示它们在双重整合器系统上的用途，以及带有黑盒神经网络控制器的Cart-Pole系统。
We present algorithms for performing data-driven stochastic reachability as an addition to SReachTools, an open-source stochastic reachability toolbox. Our method leverages a class of machine learning techniques known as kernel embeddings of distributions to approximate the safety probabilities for a wide variety of stochastic reachability problems. By representing the probability distributions of the system state as elements in a reproducing kernel Hilbert space, we can learn the "best fit" distribution via a simple regularized least-squares problem, and then compute the stochastic reachability safety probabilities as simple linear operations. This technique admits finite sample bounds and has known convergence in probability. We implement these methods as part of SReachTools, and demonstrate their use on a double integrator system, on a million-dimensional repeated planar quadrotor system, and a cart-pole system with a black-box neural network controller.
