An agent operating in an unknown dynamical system must learn its dynamics from observations. Active information gathering accelerates this learning, but existing methods derive bespoke costs for specific modeling choices: dynamics models, belief update procedures, observation models, and planners. We present a unifying framework that decouples these choices from the information-gathering cost by explicitly exposing the causal dependencies between parameters, beliefs, and controls. Using this framework, we derive a general information-gathering cost based on Massey's directed information that assumes only Markov dynamics with additive noise and is otherwise agnostic to modeling choices. We prove that the mutual information cost used in existing literature is a special case of our cost. Then, we leverage our framework to establish an explicit connection between the mutual information cost and information gain in linearized Bayesian estimation, thereby providing theoretical justification for mutual information-based active learning approaches. Finally, we illustrate the practical utility of our framework through experiments spanning linear, nonlinear, and multi-agent systems.

翻译：在未知动态系统中运行的智能体必须通过观测来学习系统动态。主动信息采集能够加速这一学习过程，但现有方法仅针对特定建模选择（包括动态模型、信念更新过程、观测模型和规划器）推导出定制化的成本函数。本文提出了一种统一框架，通过显式揭示参数、信念与控制之间的因果依赖关系，将上述建模选择与信息采集成本解耦。基于该框架，我们推导出一种基于马西有向信息的通用信息采集成本函数，该函数仅假设动态系统具有加性噪声的马尔可夫特性，而对其他建模选择保持中立。我们证明了现有文献中使用的互信息成本是本成本函数的特例。进而，我们利用该框架在互信息成本与线性化贝叶斯估计中的信息增益之间建立了显式联系，从而为基于互信息的主动学习方法提供了理论依据。最后，我们通过涵盖线性系统、非线性系统及多智能体系统的实验，展示了该框架的实际应用价值。