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：本文介绍一种利用屏障证书从数据中识别随机系统（具有未知动力学）最大安全策略集的方法。首先通过高斯过程回归学习系统动力学，并获取该估计的概率误差界限。随后，我们开发一种算法，利用学习到的高斯过程模型构建分段随机屏障函数，通过顺序剪除最差控制策略直至识别出最大策略集，从而找到最大许可策略集。该方法保证真实系统在概率意义上保持安全。这对于具有学习能力的系统尤为重要，因为丰富的策略空间能够在确保安全性的同时支持额外数据采集和复杂行为。通过对线性和非线性系统的案例研究证明，增加学习系统的数据集规模可扩大许可策略集。