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72 Artificial Intelligence for the Internet of Everything

one that has the smaller free energy), and thus is an ultimate measure of fit-
ness,or congruence,or match between the agent and its environment.

4.2.4 Behavior Workflow and Computational Considerations
Fig. 4.1 depicts a simplified schematic of the resulting cycle of sensing, con-
trol, and perception in adaptive agents, where posterior expectations (about
the hidden causes of observation inputs) minimize free energy and prescribe
actions. A team of agents differs from a single agent model by distributing the
observations, perceptions, and actions among multiple agents, while allow-
ing the agents to communicate to achieve team-level goals.
The key benefit of using the information-theoretic free-energy principle
for modeling dynamical systems is that the function lnp(s,ojm) can have a
simple mathematical structure when generative density p(s,ojm) factors out:
1 Y
φ s i , o i Þ,
Z
ps, oj mÞ ¼ i ð
ð
i
where {s i ,o i } represent the subsets of state and observation variables, φ i are
factor functions encoding dependency relations among the corresponding
variables, and Z is the normalization constant. Usually functions φ i ( ) are
simple, typically describing the relations among one to four variables at a
time. Then the agent, or team, or agents can minimize their energy with
respect to internal state (recognition density q(sjb)) using a generalized belief
propagation (BP) algorithm (Friston et al., 2013), an iterative procedure
based on message passing. Moreover, using a standard BP algorithm, derived
from a Bethe approximation to the variational free energy (Yedidia, Free-
man, & Weiss, 2005), the agents can obtain the approximating density in

(A) (B)
Fig. 4.1 Schematic of the interdependencies among variables of adaptive agent and
team models. (A) Model of a single agent. (B) Model of a team of agents.