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, 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 the message passing approach to synthetic AIF induces epistemic behaviour on a T-maze navigation task. Extension of the T-maze simulation to 1) learning goal statistics, and 2) a multi-agent bargaining setting, illustrate how this approach encourages reuse of nodes and updates in alternative settings. 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）智能体描述为通过最小化与其环境生成模型相关的变分自由能（FE）。主动推理（AIF）是FEP的一个推论，描述了智能体如何通过最小化期望自由能目标来探索和利用其环境。在两篇相关论文中，我们通过自由形式福尼式因子图（FFG）上的消息传递，描述了一种可扩展的、认知性的合成主动推理方法。一篇配套论文（第一部分）引入了约束FFG（CFFG）表示法，以可视化方式表示主动推理的（广义）自由能目标。本文（第二部分）推导了通过变分微积分在CFFG上最小化（广义）自由能目标的消息传递算法。模拟Bethe自由能与广义自由能智能体之间的比较，说明了消息传递方法如何在T型迷宫导航任务中诱导出认知行为。将T型迷宫模拟扩展至1）学习目标统计量，以及2）多智能体议价环境，展示了该方法如何促进节点与更新在不同场景中的复用。通过对合成主动推理智能体进行完整的消息传递描述，可以跨模型推导和复用消息更新，从而更接近合成主动推理的工业应用。