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 full EFE-based planning outperforms ablations that omit either the planning correction or the epistemic corrections.

翻译：主动推理将决策制定视为推理过程，其中期望自由能（EFE）统一了目标导向行为和信息寻求行为。近期研究表明，EFE最小化可被表述为对增广了认知先验的生成模型进行变分自由能（VFE）最小化。我们证明，该增广模型的VFE可改写为预测模型的VFE加上显式熵修正项，从而清晰揭示EFE的贡献机制。进一步证明，基于EFE的合理规划需要将这些认知修正与规划修正相结合——后者可将边际推理转化为策略优化，由此得出基于EFE规划的完整变分表征。这厘清了交叉熵规划与完整EFE规划各自所需的修正项。同一熵修正框架还催生了基于EFE规划的详细消息传递方案及其简化消融模型。在三个网格世界环境中的实验表明，完整EFE规划的性能优于忽略规划修正或认知修正的消融变体。