  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. At the end of the paper, an
illustrative example of optimal feedback design using deep learning is given.
