Application of the Free Energy Principle to Estimation and Control

TL;DR

This paper explores how the free energy principle (FEP) can be applied to estimation and control tasks, revealing connections to stochastic optimal control and demonstrating its effectiveness in linear Gaussian systems.

Contribution

It establishes a theoretical link between active inference based on FEP and stochastic optimal control, showing they can produce equivalent solutions under certain conditions.

Findings

Active inference incorporates both surprise minimization and control costs.

Under linear Gaussian assumptions, active inference matches classical control solutions.

Performance of active inference varies with system parameters, comparable to traditional methods.

Abstract

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.