Planning to avoid ambiguous states through Gaussian approximations to non-linear sensors in active inference agents

TL;DR

This paper investigates how Gaussian approximations to non-linear sensor models influence active inference agents' state estimation, showing that curvature-sensitive approximations induce state preferences and improve planning in robot navigation.

Contribution

It introduces a curvature-sensitive Gaussian approximation method that accounts for state-dependent ambiguities in non-linear sensor models within active inference frameworks.

Findings

Curvature-sensitive Gaussian approximations induce state-dependent ambiguity terms.

Agents prefer states with more accurate inference from observations.

Improved robot navigation planning demonstrated with the proposed method.

Abstract

In nature, active inference agents must learn how observations of the world represent the state of the agent. In engineering, the physics behind sensors is often known reasonably accurately and measurement functions can be incorporated into generative models. When a measurement function is non-linear, the transformed variable is typically approximated with a Gaussian distribution to ensure tractable inference. We show that Gaussian approximations that are sensitive to the curvature of the measurement function, such as a second-order Taylor approximation, produce a state-dependent ambiguity term. This induces a preference over states, based on how accurately the state can be inferred from the observation. We demonstrate this preference with a robot navigation experiment where agents plan trajectories.