论文标题
使用希尔伯特空间嵌入数据驱动数据驱动的随机可达性的国家置信度范围
State-Based Confidence Bounds for Data-Driven Stochastic Reachability Using Hilbert Space Embeddings
论文作者
论文摘要
在本文中，我们计算有限的样本边界，以进行数据驱动的解决方案的近似值，以解决随机可及性问题。我们的方法使用一种非参数技术，称为内核分布嵌入，并以无模型方式为随机系统提供安全性的概率保证。通过将马尔可夫控制过程的随机内核隐式嵌入在繁殖Hilbert空间中，我们可以近似具有任意随机干扰的随机系统的安全概率，即简单的矩阵操作和内部产品。我们通过构建状态和输入依赖性的概率置信范围来提出有限的样品界限，以实现安全概率的基于点的近似值。这种方法的一个优点是，边界对不均匀采样的数据有响应，这意味着在状态和输入空间的区域中，更紧密的界限是可行的，并具有更多的观察结果。我们通过数值评估该方法，并证明其在神经网络控制的摆系统上的功效。
In this paper, we compute finite sample bounds for data-driven approximations of the solution to stochastic reachability problems. Our approach uses a nonparametric technique known as kernel distribution embeddings, and provides probabilistic assurances of safety for stochastic systems in a model-free manner. By implicitly embedding the stochastic kernel of a Markov control process in a reproducing kernel Hilbert space, we can approximate the safety probabilities for stochastic systems with arbitrary stochastic disturbances as simple matrix operations and inner products. We present finite sample bounds for point-based approximations of the safety probabilities through construction of probabilistic confidence bounds that are state- and input-dependent. One advantage of this approach is that the bounds are responsive to non-uniformly sampled data, meaning that tighter bounds are feasible in regions of the state- and input-space with more observations. We numerically evaluate the approach, and demonstrate its efficacy on a neural network-controlled pendulum system.
