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.

通过使用障碍证明方法，结合高斯过程回归，本文介绍了一种从具备未知动力学的随机系统数据中鉴定出一组最大安全策略的方法。通过学习系统动力学并得到该预估的概率误差，我们开发了一种算法来构建分段随机障碍函数，从而利用学习到的高斯过程模型找到一组最大允许的策略集，该集合通过有序地剔除最糟糕的控制策略直至得到最大集合，保证了真实系统的概率安全性。这对于学习能力系统而言尤为重要，因为丰富的策略空间不仅可以增加数据采集，还能保持安全性并展现复杂行为。线性和非线性系统的案例研究表明，扩大用于学习系统的数据集大小能够增加最大允许的策略集。