The Free Energy Principle (FEP) describes (biological) agents as minimising a variational Free Energy (FE) with respect to a generative model of their environment. Active Inference (AIF) is a corollary of the FEP that describes how agents explore and exploit their environment by minimising an expected FE objective. In two related papers, we describe a scalable, epistemic approach to synthetic AIF agents, by message passing on free-form Forney-style Factor Graphs (FFGs). A companion paper (part I) introduces a Constrained FFG (CFFG) notation that visually represents (generalised) FE objectives for AIF. The current paper (part II) derives message passing algorithms that minimise (generalised) FE objectives on a CFFG by variational calculus. A comparison between simulated Bethe and generalised FE agents illustrates how synthetic AIF induces epistemic behaviour on a T-maze navigation task. With a full message passing account of synthetic AIF agents, it becomes possible to derive and reuse message updates across models and move closer to industrial applications of synthetic AIF.

翻译：自由能原理（FEP）将（生物）代理描述为相对于其环境生成模型最小化变分自由能（FE）的实体。主动推理（AIF）是FEP的一个推论，描述了代理如何通过最小化期望FE目标来探索和利用其环境。在两篇相关论文中，我们描述了一种通过自由形式Forney风格因子图（FFG）上的消息传递来实现可扩展、认识论的合成AIF代理的方法。配套论文（第一部分）介绍了约束FFG（CFFG）表示法，该表示法以可视化方式表示AIF的（广义）FE目标。当前论文（第二部分）通过变分法推导出在CFFG上最小化（广义）FE目标的消息传递算法。模拟Bethe与广义FE代理之间的比较展示了合成AIF如何在T型迷宫导航任务中诱导认识论行为。通过完整的合成AIF代理消息传递描述，可以跨模型推导并重用消息更新，从而更接近合成AIF的工业应用。