What Type of Inference is Active Inference?
For researchers in active inference and decision-making, this work clarifies the theoretical relationship between EFE and VFE, offering a unified framework and practical message-passing schemes.
The paper provides a variational formalization of Expected Free Energy (EFE) minimization in active inference, showing it reduces to Variational Free Energy (VFE) minimization with explicit entropy corrections. Experiments on grid-world tasks demonstrate that a planning correction improves performance with decisive observations, while epistemic corrections are crucial for suggestive observations.
Active inference casts decision-making as inference, with the Expected Free Energy (EFE) unifying goal-directed and information-seeking behavior. Recent work showed that EFE minimization can be written as Variational Free Energy (VFE) minimization on a generative model augmented with epistemic priors. We prove that the VFE of the augmented model can be rewritten as the VFE of the predictive model plus explicit entropy-correction terms, making the EFE contribution transparent. We then show that proper EFE-based planning requires combining these epistemic corrections with a planning correction that turns marginal inference into policy optimization, yielding a full variational characterization of EFE-based planning. This clarifies which corrections are needed for cross-entropy planning and for full EFE-based planning. The same entropy-corrected formulation leads to a detailed message-passing scheme for EFE-based planning together with simpler ablations. Experiments on three grid-world environments show that the planning correction already helps when observations are decisive, whereas the additional observation-side epistemic corrections matter most when observations are merely suggestive.