  Recently, new approaches to adaptive control have sought to reformulate the
problem as a minimization of a relative entropy criterion to obtain tractable
solutions. In particular, it has been shown that minimizing the expected
deviation from the causal input-output dependencies of the true plant leads to
a new promising stochastic control rule called the Bayesian control rule. This
work proves the convergence of the Bayesian control rule under two sufficient
assumptions: boundedness, which is an ergodicity condition; and consistency,
which is an instantiation of the sure-thing principle.
