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的生成模型最小化变分自由能（FE）。主动推理（AIF）是FEP的一个推论，描述了代理如何通过最小化预期FE目标来探索和利用其环境。在两篇相关论文中，我们提出了一种可扩展的、基于认知的合成AIF代理方法，该方法通过在自由形式Forney风格因子图（FFGs）上进行消息传递来实现。姊妹篇（第一部分）引入了一种约束FFG（CFFG）符号，该符号直观地表示了AIF的（广义）FE目标。当前论文（第二部分）通过变分计算推导出了在CFFG上最小化（广义）FE目标的消息传递算法。模拟的Bethe代理与广义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知行为。通过对合成AIF代理的完整消息传递分析，使得跨模型推导和重用消息更新成为可能，从而向合成AIF的工业应用迈进了一步。