Studies of how people learn to solve puzzles I would like to build a cognitive model that is able to learn how to solve a complex puzzle such as the tower of Hanoi based off of limited feed-back (set of valid moves, closer to goal, farther from goal). I have found some references for learning the Tower of Hanoi and the performance of schizophrenics, but I was wondering if there was a particular name for the type of learning I'm looking for (advanced reinforcement learning?) and if there are further studies on how people learn these types of puzzles.
I'm not sure if this is what you are looking for, but the big umbrella term in the literature for puzzles like the Tower of Hanoi is problem solving. 

A Google Scholar search for "tower of hanoi" and "problem solving" generates ~5000 hits. Another related puzzle is the Tower of London, and that Scholar search generates an additional ~5000.