  Active Inference (ActInf) is an emerging theory that explains perception and
action in biological agents, in terms of minimizing a free energy bound on
Bayesian surprise. Goal-directed behavior is elicited by introducing prior
beliefs on the underlying generative model. In contrast to prior beliefs, which
constrain all realizations of a random variable, we propose an alternative
approach through chance constraints, which allow for a (typically small)
probability of constraint violation, and demonstrate how such constraints can
be used as intrinsic drivers for goal-directed behavior in ActInf. We
illustrate how chance-constrained ActInf weights all imposed (prior)
constraints on the generative model, allowing e.g., for a trade-off between
robust control and empirical chance constraint violation. Secondly, we
interpret the proposed solution within a message passing framework.
Interestingly, the message passing interpretation is not only relevant to the
context of ActInf, but also provides a general purpose approach that can
account for chance constraints on graphical models. The chance constraint
message updates can then be readily combined with other pre-derived message
update rules, without the need for custom derivations. The proposed
chance-constrained message passing framework thus accelerates the search for
workable models in general, and can be used to complement message-passing
formulations on generative neural models.
