Compositionality of optimal control laws

We present a theory of compositionality in stochastic optimal control, showing how task-optimal controllers can be constructed from certain primitives. The primitives are themselves feedback controllers pursuing their own agendas. They are mixed in proportion to how much progress they are making towards their agendas and how compatible their agendas are with the present task. The resulting composite control law is provably optimal when the problem belongs to a certain class. This class is rather general and yet has a number of unique properties - one of which is that the Bellman equation can be made linear even for non-linear or discrete dynamics.