Active inference is a mathematical framework for understanding how agents (biological or artificial) interact with their environments, enabling continual adaptation and decision-making. It combines Bayesian inference and free energy minimization to model perception, action, and learning in uncertain and dynamic contexts. Unlike reinforcement learning, active inference integrates exploration and exploitation seamlessly by minimizing expected free energy. In this paper, we present a continual learning framework for agents operating in discrete time environments, using active inference as the foundation. We derive the mathematical formulations of variational and expected free energy and apply them to the design of a self-learning research agent. This agent updates its beliefs and adapts its actions based on new data without manual intervention. Through experiments in changing environments, we demonstrate the agent's ability to relearn and refine its models efficiently, making it suitable for complex domains like finance and healthcare. The paper concludes by discussing how the proposed framework generalizes to other systems, positioning active inference as a flexible approach for adaptive AI.

本文针对主动推理在复杂动态环境中应用的研究空白，提出了一种基于主动推理的持续学习框架，允许代理自我学习和适应。通过数学公式推导，作者展示了该代理如何在不断变化的环境中高效重新学习并优化其模型，具有在金融和医疗等复杂领域的潜在应用价值。

展示离散时间主动推理的持续学习能力及实际应用