  In Hierarchical Control, compositionality, abstraction, and task-transfer are
crucial for designing versatile algorithms which can solve a variety of
problems with maximal representational reuse. We propose a novel hierarchical
and compositional framework called Jump-Operator Dynamic Programming for
quickly computing solutions within a super-exponential space of sequential
sub-goal tasks with ordering constraints, while also providing a fast
linearly-solvable algorithm as an implementation. This approach involves
controlling over an ensemble of reusable goal-conditioned polices functioning
as temporally extended actions, and utilizes transition operators called
feasibility functions, which are used to summarize initial-to-final state
dynamics of the polices. Consequently, the added complexity of grounding a
high-level task space onto a larger ambient state-space can be mitigated by
optimizing in a lower-dimensional subspace defined by the grounding,
substantially improving the scalability of the algorithm while effecting
transferable solutions. We then identify classes of objective functions on this
subspace whose solutions are invariant to the grounding, resulting in optimal
zero-shot transfer.
