  Based on a generative model (GM) and beliefs over hidden states, the free
energy principle (FEP) enables an agent to sense and act by minimizing a free
energy bound on Bayesian surprise. Inclusion of prior beliefs in the GM about
desired states leads to active inference (ActInf). In this work, we aim to
reveal connections between ActInf and stochastic optimal control. We reveal
that, in contrast to standard cost and constraint-based solutions, ActInf gives
rise to a minimization problem that includes both an information-theoretic
surprise term and a model-predictive control cost term. We further show under
which conditions both methodologies yield the same solution for estimation and
control. For a case with linear Gaussian dynamics and a quadratic cost, we
illustrate the performance of ActInf under varying system parameters and
compare to classical solutions for estimation and control.
