  Most known regret bounds for reinforcement learning are either episodic or
assume an environment without traps. We derive a regret bound without making
either assumption, by allowing the algorithm to occasionally delegate an action
to an external advisor. We thus arrive at a setting of active one-shot
model-based reinforcement learning that we call DRL (delegative reinforcement
learning.) The algorithm we construct in order to demonstrate the regret bound
is a variant of Posterior Sampling Reinforcement Learning supplemented by a
subroutine that decides which actions should be delegated. The algorithm is not
anytime, since the parameters must be adjusted according to the target time
discount. Currently, our analysis is limited to Markov decision processes with
finite numbers of hypotheses, states and actions.
