Expected free energy as an information constraint on the Bethe Lagrangian

2026-08-17

AI Summary

该研究通过引入基于Bethe自由能函数和信息约束的方法，解决了在主动推理中因未观测结果导致的KL散度结构缺失问题。

Abstract

Active inference selects actions by minimising an expected free energy functional over predicted futures. However, adding an expectation over yet-unobserved outcomes means the free energy functional no longer has a Kullback-Leibler structure, which hinders message passing treatments of inference procedures. We propose an alternative formulation based on a Bethe free energy functional, fully supporting inference by message passing. The epistemic drive is maintained by imposing an information constraint, next to normalisation, marginalisation and form constraints, insisting that the mutual information between future observations, states and parameters given actions must be at least as large as the entropy of the goal prior. For a specific value of the corresponding Karush-Kuhn-Tucker multiplier, the stationary point of this constrained Bethe Lagrangian recovers the expected free energy solution. We show that, as the information demand is varied, the solved multiplier moves through its inactive, interior, and saturated regimes. In the inactive regime the agent's epistemic drive switches off entirely, while in the saturated regime it is maximal. We compare the performance of the constrained Bethe agent on three tasks against EFE and Q-MDP.

Problem

• active inference
• expected free energy
• Bethe free energy
• message passing
• information constraint

Innovation

• Bethe free energy
• information constraint
• message passing
• expected free energy
• epistemic drive