Many engineering and scientific workflows depend on expensive black-box evaluations, requiring decision-making that simultaneously improves performance and reduces uncertainty. Bayesian optimization (BO) and Bayesian experimental design (BED) offer powerful yet largely separate treatments of goal-seeking and information-seeking, providing limited guidance for hybrid settings where learning and optimization are intrinsically coupled. We propose "pragmatic curiosity," a hybrid learning-optimization paradigm derived from active inference, in which actions are selected by minimizing the expected free energy--a single objective that couples pragmatic utility with epistemic information gain. We demonstrate the practical effectiveness and flexibility of pragmatic curiosity on various real-world hybrid tasks, including constrained system identification, targeted active search, and composite optimization with unknown preferences. Across these benchmarks, pragmatic curiosity consistently outperforms strong BO-type and BED-type baselines, delivering higher estimation accuracy, better critical-region coverage, and improved final solution quality.

翻译：许多工程与科学工作流依赖于昂贵的黑箱评估，这要求决策过程在提升性能的同时降低不确定性。贝叶斯优化（BO）与贝叶斯实验设计（BED）分别为目标导向与信息导向提供了强大但基本独立的处理框架，对于学习和优化本质耦合的混合场景则缺乏有效指导。我们提出“实用好奇心”——一种源自主动推理的混合学习-优化范式，其通过最小化期望自由能来选择行动，该单一目标将实用效用与认知信息增益相耦合。我们在多种现实混合任务中验证了实用好奇心的实际效能与灵活性，包括约束系统辨识、定向主动搜索以及未知偏好下的复合优化。在这些基准测试中，实用好奇心持续超越贝叶斯优化型与贝叶斯实验设计型基线方法，展现出更高的估计精度、更优的关键区域覆盖度以及更佳的最终解质量。