The importance of hierarchically structured representations for tractable planning has long been acknowledged. However, the questions of how people discover such abstractions and how to define a set of optimal abstractions remain open. This problem has been explored in cognitive science in the problem solving literature and in computer science in hierarchical reinforcement learning. Here, we emphasize an algorithmic perspective on learning hierarchical representations in which the objective is to efficiently encode the structure of the problem, or, equivalently, to learn an algorithm with minimal length. We introduce a novel problem-solving paradigm that links problem solving and program induction under the Markov Decision Process (MDP) framework. Using this task, we target the question of whether humans discover hierarchical solutions by maximizing efficiency in number of actions they generate or by minimizing the complexity of the resulting representation and find evidence for the primacy of representational efficiency.
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