Active inference is a leading theory of perception, learning and decision making, which can be applied to neuroscience, robotics, psychology, and machine learning. Active inference is based on the expected free energy, which is mostly justified by the intuitive plausibility of its formulations, e.g., the risk plus ambiguity and information gain / pragmatic value formulations. This paper seek to formalize the problem of deriving these formulations from a single root expected free energy definition, i.e., the unification problem. Then, we study two settings, each one having its own root expected free energy definition. In the first setting, no justification for the expected free energy has been proposed to date, but all the formulations can be recovered from it. However, in this setting, the agent cannot have arbitrary prior preferences over observations. Indeed, only a limited class of prior preferences over observations is compatible with the likelihood mapping of the generative model. In the second setting, a justification of the root expected free energy definition is known, but this setting only accounts for two formulations, i.e., the risk over states plus ambiguity and entropy plus expected energy formulations.

翻译：主动推理是感知、学习与决策领域的前沿理论，可应用于神经科学、机器人学、心理学及机器学习。该理论基于预期自由能，其合理性主要源于公式的直观解释力，例如风险与模糊性公式、信息增益与实用价值公式等。本文旨在系统解决从单一预期自由能基础公式推导出这些衍生公式的问题，即统一性问题。我们进而研究两种框架，每种框架均具有各自的基础预期自由能定义。在第一种框架中，目前尚未提出预期自由能的合理性依据，但所有衍生公式均可由此基础公式推导得出。然而在该框架下，智能体无法对观测结果施加任意先验偏好，仅有与生成模型的似然映射兼容的有限类别先验观测偏好成立。在第二种框架中，虽已知基础预期自由能定义的理论依据，但该框架仅能解释两种衍生公式，即状态风险与模糊性公式、熵与预期能量公式。