On Kalman-Bucy filters, linear quadratic control and active inference

TL;DR

This paper compares Kalman-Bucy filters, linear quadratic control, and active inference, highlighting their similarities and differences in modeling sensorimotor control in biological systems.

Contribution

It provides a detailed comparison of the mathematical frameworks of LQG and active inference for linear systems, emphasizing their assumptions and distinctions.

Findings

Both frameworks use similar mathematical formalisms.

Active inference incorporates biased perception, unlike LQG.

The paper clarifies the conceptual differences in sensorimotor control models.

Abstract

Linear Quadratic Gaussian (LQG) control is a framework first introduced in control theory that provides an optimal solution to linear problems of regulation in the presence of uncertainty. This framework combines Kalman-Bucy filters for the estimation of hidden states with Linear Quadratic Regulators for the control of their dynamics. Nowadays, LQG is also a common paradigm in neuroscience, where it is used to characterise different approaches to sensorimotor control based on state estimators, forward and inverse models. According to this paradigm, perception can be seen as a process of Bayesian inference and action as a process of optimal control. Recently, active inference has been introduced as a process theory derived from a variational approximation of Bayesian inference problems that describes, among others, perception and action in terms of (variational and expected) free energy minimisation. Active inference relies on a mathematical formalism similar to LQG, but offers a rather different perspective on problems of sensorimotor control in biological systems based on a process of biased perception. In this note we compare the mathematical treatments of these two frameworks for linear systems, focusing on their respective assumptions and highlighting their commonalities and technical differences.