  Adaptive control problems are notoriously difficult to solve even in the
presence of plant-specific controllers. One way to by-pass the intractable
computation of the optimal policy is to restate the adaptive control as the
minimization of the relative entropy of a controller that ignores the true
plant dynamics from an informed controller. The solution is given by the
Bayesian control rule-a set of equations characterizing a stochastic adaptive
controller for the class of possible plant dynamics. Here, the Bayesian control
rule is applied to derive BCR-MDP, a controller to solve undiscounted Markov
decision processes with finite state and action spaces and unknown dynamics. In
particular, we derive a non-parametric conjugate prior distribution over the
policy space that encapsulates the agent's whole relevant history and we
present a Gibbs sampler to draw random policies from this distribution.
Preliminary results show that BCR-MDP successfully avoids sub-optimal limit
cycles due to its built-in mechanism to balance exploration versus
exploitation.
