  Active inference is a leading theory of perception, learning and decision
making, which can be applied to neuroscience, robotics, psychology, and machine
learning. Active inference is based on the expected free energy, which is
mostly justified by the intuitive plausibility of its formulations, e.g., the
risk plus ambiguity and information gain / pragmatic value formulations. This
paper seek to formalize the problem of deriving these formulations from a
single root expected free energy definition, i.e., the unification problem.
Then, we study two settings, each one having its own root expected free energy
definition. In the first setting, no justification for the expected free energy
has been proposed to date, but all the formulations can be recovered from it.
However, in this setting, the agent cannot have arbitrary prior preferences
over observations. Indeed, only a limited class of prior preferences over
observations is compatible with the likelihood mapping of the generative model.
In the second setting, a justification of the root expected free energy
definition is known, but this setting only accounts for two formulations, i.e.,
the risk over states plus ambiguity and entropy plus expected energy
formulations.
