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Active Inference in Multiagent Systems 69

upper bound on the entropy of its outcomes—or the sensory states—it sam-
ples. Consequently, the free energy principle provides a mathematical foun-
dation to explain how agents maintain order by restricting themselves to a
limited number of states. This framework gives a formal mechanism to
design decentralized purpose-driven behaviors, where multiple agents can
operate autonomously to resist disorder without supervised control by
external agents but have a potential for peer-to-peer collaboration and
competition.

4.2.2 Adaptive Behavior and Context
Free energy generalizes to learning and cognition, prescribing the acquisi-
tion of any form of knowledge as an attempt to reduce surprise. Moreover,
a fundamental property of this formulation, as can be seen below with its
mathematical derivations, is that both free energy and the surprise it bounds
are highly contextual. First, surprise is a function of sensations and the agent
predicting them, existing only in relation to model-based expectations.
Surprise-minimizing agents attempt to adapt to the context contained in
their observations. Second, the free energy principle suggests that agents har-
vest the sensory signals they can predict, keeping to consistent subspaces of
the physical and physiological variables that define their existence (Friston,
Thornton, & Clark, 2012). When the perceptions about the world are con-
stant, minimization of the energy makes the agents change their actions to
maximize the entropy of the sensations (and, accordingly, self-information)
they receive. In other words, the adaptive behaviors prescribed by the free
energy principle tightly couple the environment and the agents that populate
it and conform to the expectations of those behaviors.
Further, the minimization of surprise suggests that the selected adaptive
actions cannot be deterministic. These reflections provide a key differenti-
ation between the behaviors based on the free-energy principle and the clas-
sical control formulations where utility or cost functions are optimized.
Essentially, the contextual information encoded by free energy produces
stochastic actions to achieve a boundedly rational behavior.
The concept of surprise minimization is the basis for many modern esti-
mation theories, system identification, anomaly detection, and adaptive con-
trol (e.g., Bar-Shalom, Li, & Kirubarajan, 2004; Ljung & Glad, 1994). Ideas
similar to the free-energy principle have also been pursued in manual control
and normative-descriptive models of human decision making. For example,
the internal model control (IMC) principles of control theory state that