Deriving Time-Averaged Active Inference from Control Principles

Active inference offers a principled account of behavior as minimizing average sensory surprise over time. Applications of active inference to control problems have heretofore tended to focus on finite-horizon or discounted-surprise problems, despite deriving from the infinite-horizon, average-surprise imperative of the free-energy principle. Here we derive an infinite-horizon, average-surprise formulation of active inference from optimal control principles. Our formulation returns to the roots of active inference in neuroanatomy and neurophysiology, formally reconnecting active inference to optimal feedback control. Our formulation provides a unified objective functional for sensorimotor control and allows for reference states to vary over time.

Automated summary

Active inference explains behavior by minimizing the average surprise of sensations. Previous applications of active inference in control problems have mainly focused on finite or discounted surprise, rather than the infinite-horizon and average-surprise requirement of the free-energy principle. In this paper, we derive an infinite-horizon and average-surprise formulation of active inference from optimal control principles. Our formulation reestablishes the connection between active inference and neuroanatomy, neurophysiology, and optimal feedback control, and provides a unified objective functional for sensorimotor control that allows for time-varying reference states.