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In Hierarchical Control, compositionality, abstraction, and task-transfer arecrucial for designing versatile algorithms which can solve a variety ofproblems with maximal representational reuse. We propose a novel hierarchicaland compositional framework called Jump-Operator Dynamic Programming forquickly computing solutions within a super-exponential space of sequentialsub-goal tasks with ordering constraints, while also providing a fastlinearly-solvable algorithm as an implementation. This approach involvescontrolling over an ensemble of reusable goal-conditioned polices functioningas temporally extended actions, and utilizes transition operators calledfeasibility functions, which are used to summarize initial-to-final statedynamics of the polices. Consequently, the added complexity of grounding ahigh-level task space onto a larger ambient state-space can be mitigated byoptimizing in a lower-dimensional subspace defined by the grounding,substantially improving the scalability of the algorithm while effectingtransferable solutions. We then identify classes of objective functions on thissubspace whose solutions are invariant to the grounding, resulting in optimalzero-shot transfer.

Jump Operator Planning: Goal-Conditioned Policy Ensembles and Zero-Shot Transfer