  We study reinforcement learning for the optimal control of Branching Markov
Decision Processes (BMDPs), a natural extension of (multitype) Branching Markov
Chains (BMCs). The state of a (discrete-time) BMCs is a collection of entities
of various types that, while spawning other entities, generate a payoff. In
comparison with BMCs, where the evolution of a each entity of the same type
follows the same probabilistic pattern, BMDPs allow an external controller to
pick from a range of options. This permits us to study the best/worst behaviour
of the system. We generalise model-free reinforcement learning techniques to
compute an optimal control strategy of an unknown BMDP in the limit. We present
results of an implementation that demonstrate the practicality of the approach.
