When are tasks “difficult” for learning controllers?

Some control task, formerly believed to be difficult and used to demonstrate neural network unsupervised learning, can be accomplished with very simple controllers. There seems to be no learning method that discovers these controllers. This failure could be attributed to the learning algorithm or to starting with overly complex controller structures. We suggest using the probability that randomly selected controller is successful as measure of learning difficulty. To limit the size of the space of possible controllers we use Fliess´ classification of control problems into flat and non-flat. We illustrate the procedure on easy and difficult variants of the pendulum control task