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Hierarchical reinforcement learning methods offer a powerful means ofplanning flexible behavior in complicated domains. However, learning anappropriate hierarchical decomposition of a domain into subtasks remains asubstantial challenge. We present a novel algorithm for subtask discovery,based on the recently introduced multitask linearly-solvable Markov decisionprocess (MLMDP) framework. The MLMDP can perform never-before-seen tasks byrepresenting them as a linear combination of a previously learned basis set oftasks. In this setting, the subtask discovery problem can naturally be posed asfinding an optimal low-rank approximation of the set of tasks the agent willface in a domain. We use non-negative matrix factorization to discover thisminimal basis set of tasks, and show that the technique learns intuitivedecompositions in a variety of domains. Our method has several qualitativelydesirable features: it is not limited to learning subtasks with single goalstates, instead learning distributed patterns of preferred states; it learnsqualitatively different hierarchical decompositions in the same domaindepending on the ensemble of tasks the agent will face; and it may bestraightforwardly iterated to obtain deeper hierarchical decompositions.

Hierarchical Subtask Discovery With Non-Negative Matrix Factorization