Can supervised learning be used to solve the inverted pendulum problem? I know that reinforcement learning has been used to solve the inverted pendulum problem.

Can supervised learning be used to solve the inverted pendulum problem? 

For example, there could be an interface (e.g. a joystick) with the cart-pole system, which the human can use to balance the pole and, at the same time, collect a dataset for supervised learning. Has this been done before?
Of course, you can, and yes this has been researched and done before. By using supervised learning, you give the machine some data, and it will try to figure the best way to analyze and predict the next movement in case of an inverted pendulum problem.
I found a complete paper for this problem: Neural network control of an inverted pendulum on a cart by Valeri Mladenov et al.