Recent research reveals that deep learning is an effective way of solving high dimensional Hamilton–Jacobi–Bellman equations. The resulting feedback control law in the form of a neural network is computationally efficient for real-time applications of optimal control. A critical part of this design method is to generate data for training the neural network and validating its accuracy. In this paper, we provide a survey of existing algorithms that can be used to generate data. All the algorithms surveyed in this paper are causality-free, i.e., the solution at a point is computed without using the value of the function at any other points. An illustrative example is given for the optimal feedback design using supervised learning in which the data is generated using causality-free algorithms.

最近的研究表明，深度学习是求解高维 Hamilton-Jacobi-Bellman 方程的有效方法。由此产生的神经网络形式的反馈控制律对于最优控制的实时应用在计算上是有效的。这种设计方法的一个关键部分是生成用于训练神经网络和验证其准确性的数据。在本文中，我们对可用于生成数据的现有算法进行了调查。本文中调查的所有算法都是无因果关系的，即在不使用任何其他点的函数值的情况下计算某一点的解。给出了使用监督学习的最佳反馈设计的说明性示例，其中使用无因果关系算法生成数据。