  Active inference, a corollary of the free energy principle, is a formal way
of describing the behavior of certain kinds of random dynamical systems that
have the appearance of sentience. In this chapter, we describe how active
inference combines Bayesian decision theory and optimal Bayesian design
principles under a single imperative to minimize expected free energy. It is
this aspect of active inference that allows for the natural emergence of
information-seeking behavior. When removing prior outcomes preferences from
expected free energy, active inference reduces to optimal Bayesian design,
i.e., information gain maximization. Conversely, active inference reduces to
Bayesian decision theory in the absence of ambiguity and relative risk, i.e.,
expected utility maximization. Using these limiting cases, we illustrate how
behaviors differ when agents select actions that optimize expected utility,
expected information gain, and expected free energy. Our T-maze simulations
show optimizing expected free energy produces goal-directed information-seeking
behavior while optimizing expected utility induces purely exploitive behavior
and maximizing information gain engenders intrinsically motivated behavior.
