This paper introduces a method of identifying a maximal set of safe strategies from data for stochastic systems with unknown dynamics using barrier certificates. The first step is learning the dynamics of the system via Gaussian process (GP) regression and obtaining probabilistic errors for this estimate. Then, we develop an algorithm for constructing piecewise stochastic barrier functions to find a maximal permissible strategy set using the learned GP model, which is based on sequentially pruning the worst controls until a maximal set is identified. The permissible strategies are guaranteed to maintain probabilistic safety for the true system. This is especially important for learning-enabled systems, because a rich strategy space enables additional data collection and complex behaviors while remaining safe. Case studies on linear and nonlinear systems demonstrate that increasing the size of the dataset for learning the system grows the permissible strategy set.

翻译：本文提出一种利用障碍函数从数据中识别随机系统（动态未知）的最大许可策略集的方法。首先通过高斯过程回归学习系统动态，并获取该估计的概率误差。随后，我们开发了一种基于学习的高斯过程模型构建分段随机障碍函数的算法，通过逐次剔除最差控制策略直至识别出最大策略集，从而得到最大许可策略集。该许可策略能保证真实系统的概率安全性。这一特性对具备学习能力的系统尤为重要——丰富的策略空间既能支持额外数据采集与复杂行为，又能确保系统安全。在线性与非线性系统的案例研究中表明，用于学习系统的数据集规模越大，所获得的许可策略集也越大。