Pragmatic Curiosity: A Hybrid Learning-Optimization Paradigm via Active Inference

2026-02-05

AI Summary

This work addresses the challenge of jointly optimizing performance and reducing uncertainty in engineering and scientific tasks that rely on costly black-box evaluations, particularly in hybrid scenarios where learning and optimization are tightly coupled. The authors propose a novel “pragmatic curiosity” framework that unifies Bayesian optimization and Bayesian experimental design by leveraging expected free energy from active inference as a single objective, thereby enabling coherent trade-offs between goal-directed exploitation and information-seeking exploration. Built upon Bayesian modeling and black-box optimization, this general-purpose framework demonstrates consistent superiority over existing baselines across diverse tasks—including system identification, active search, and composite optimization with unknown preferences—yielding improved solution quality, enhanced coverage of critical regions, and higher estimation accuracy.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

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.

Problem

• Bayesian optimization
• Bayesian experimental design
• active inference
• hybrid learning-optimization
• black-box evaluation

Innovation

• pragmatic curiosity
• active inference
• expected free energy
• Bayesian optimization
• Bayesian experimental design