Message passing-based inference in an autoregressive active inference agent

TL;DR

This work presents an autoregressive active inference agent implemented as message passing on a Forney-style factor graph to perform perception, planning, and learning under unknown dynamics. It derives an expected free energy objective for continuous observations and bounded actions and implements planning as a sequence of 1-step-ahead EFE minimizations linked through a planning graph. Dynamics parameters are learned via conjugate Bayesian updates under a matrix-normal–Wishart prior, with predictive planning expressed through a Laplace-approximated posterior over future observations. In robot-navigation experiments, the MARX-EFE agent achieves lower free energy and ultimately closer positioning to the goal than a standard model-predictive controller, at the cost of slower arrival, illustrating a cautious, model-learning-driven control strategy with distributed, modular inference. Together, the approach demonstrates a scalable, plug-and-play framework for active inference in continuous domains with unknown dynamics.

Abstract

We present the design of an autoregressive active inference agent in the form of message passing on a factor graph. Expected free energy is derived and distributed across a planning graph. The proposed agent is validated on a robot navigation task, demonstrating exploration and exploitation in a continuous-valued observation space with bounded continuous-valued actions. Compared to a classical optimal controller, the agent modulates action based on predictive uncertainty, arriving later but with a better model of the robot's dynamics.

Figures (4)

• Figure 1: Forney-style factor graph of one time step (separated by dots) of Bayesian filtering. Edges represent random variables and nodes operations on those variables. Black squares represent observed variables or set parameters, and the dotted box represents a custom node, composed of the nodes within. Message $1$ is the prior belief over parameters and message $2$ the likelihood-based update. These are are multiplied at the equality node, yielding the marginal posterior distribution (message $3$).
• Figure 2: Factor graph of the 1-step ahead planning model. The left half of the graph is the same as in Figure \ref{['fig:ffg-paramest']}. The parameter posterior (message $3$) is passed forwards to the MARX-EFE node, which takes in message $4$ from the goal prior node and produces message $6$ containing the exponentiated EFE function. Combined with message $5$ from the control prior node, this produces the variational control posterior. The $\delta$ circle denotes a collapse of the posterior to a Dirac delta distribution van2024realizing.
• Figure 3: Factor graph of a $4$-step ahead planning model, showing repeated MARX-EFE node from Figure \ref{['fig:ffg-planning-1step']}. Some buffer variables are now latent as well. Message $7$ is the posterior predictive over $y_t$ carrying forward system output predictions given a selection control input. Message $8$ is a predictive likelihood over $y_t$ sent backwards from the node at time $t+1$. Together the forward and backward pass of predictive messages generates a sequence of goal priors.
• Figure 4: MARX-EFE (blue) vs. MARX-MPC (red) over a trial of $1000$ seconds, compared in terms of free energy (left), Euclidean distance to goal ($m_{*}$; middle) and 2-norm of controls (right). Results are averaged over 10 experiments. MARX-EFE initially takes smaller actions, aiming to improve parameters and predictions first. It arrives at the goal later than MARX-MPC but is better able to park on the goal itself. MARX-EFE's actions are small initially but increase in magnitude as uncertainty shrinks.

Theorems & Definitions (4)

• theorem thmcountertheorem
• corollary thmcountercorollary
• proof
• proof