The problems you mention are likely an artifact of him using a bad optimzation method, not inherently a limitation in the function approximator. Ironically, its

The problems you mention are likely an artifact of him using a bad optimzation method, not inherently a limitation in the function approximator. Ironically, its most similar to genetic search, a method most commonly associated with machine learning. If he used a standard optimzation method instead, convergence would be fast and the result much better. A similar problem, using splines to set force inputs for a robot that travels through a maze with barriers optimized using start and end position and force minimization, was a lab in a course I took last year. The question becomes one of hyper parameter search, i.e. what kind of model/function approximator is sufficient. Here the problem is easy enough that its easy to find a sufficient simple model. The huge networks are nice for more general problems because they tend to work moderately well for everything... in the dataset.