Application of the Free Energy Principle to Estimation and Control
Journal article, 2021

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, i.e., the negative logarithm of the marginal likelihood. Inclusion of desired states in the form of prior beliefs in the GM 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.

Active inference

Stochastic processes

Signal processing

factor graphs

message passing

stochastic optimal control

Probabilistic logic

Optimal control

Numerical models

Probability density function



Thijs van de Laar

Eindhoven University of Technology

Ayca Ozcelikkale

Uppsala University

Henk Wymeersch

Chalmers, Electrical Engineering, Communication and Antenna Systems, Communication Systems

IEEE Transactions on Signal Processing

1053-587X (ISSN)

Vol. 69 4234-4244

Smart Sensing and Communications with Energy Harvesting

Swedish Research Council (VR) (2015-04011), 2016-01-01 -- 2019-12-31.

Multi-dimensional Signal Processing with Frequency Comb Transceivers

Swedish Research Council (VR) (2018-03701), 2018-12-01 -- 2021-12-31.

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Control Engineering



More information

Latest update

9/6/2021 9