Abstract: The application of expected utility theory to construct adaptiveagents is both computationally intractable and statistically questionable. To overcome these difficulties, agents need the ability to delay the choice of the optimal policy to a later stage when they have learned more about the environment. How should agents do this optimally? An information-theoretic answer to this question is given by the Bayesian control rule – the solution to the adaptive coding problem when there are not only observations but also actions. We review the central ideas behind the Bayesian control rule.