# Pragmatic Curiosity: A Unified Framework for Hybrid Learning and Optimization via Active Inference

arXiv: https://arxiv.org/abs/2602.06104 · HTML: https://mlsanity.com/paper/2602.06104/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 36 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Builds on (most cited first, 17 of 17)

- [YOLOv3: An Incremental Improvement](https://mlsanity.com/paper/1804.02767/) (2018)
- [CARLA: An Open Urban Driving Simulator](https://mlsanity.com/paper/1711.03938/) (2017)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Learning to Optimize via Information-Directed Sampling](https://mlsanity.com/paper/1403.5556/) (2014)
- [Scenic: A Language for Scenario Specification and Scene Generation](https://mlsanity.com/paper/1809.09310/) (2018)
- [An Easy-to-use Real-world Multi-objective Optimization Problem Suite](https://mlsanity.com/paper/2009.12867/) (2020)
- [Prediction-Oriented Bayesian Active Learning](https://mlsanity.com/paper/2304.08151/) (2023)
- [Joint Entropy Search for Maximally-Informed Bayesian Optimization](https://mlsanity.com/paper/2206.04771/) (2022)
- [Preference Exploration for Efficient Bayesian Optimization with Multiple Outcomes](https://mlsanity.com/paper/2203.11382/) (2022)
- [Bayesian Algorithm Execution: Estimating Computable Properties of Black-box Functions Using Mutual Information](https://mlsanity.com/paper/2104.09460/) (2021)
- [Failing to Learn: Autonomously Identifying Perception Failures for Self-driving Cars](https://mlsanity.com/paper/1707.00051/) (2017)
- [Self-Correcting Bayesian Optimization through Bayesian Active Learning](https://mlsanity.com/paper/2304.11005/) (2023)
- [Active Learning and Bayesian Optimization: a Unified Perspective to Learn with a Goal](https://mlsanity.com/paper/2303.01560/) (2023)
- [On the Implementation of a Bayesian Optimization Framework for Interconnected Systems](https://mlsanity.com/paper/2501.00967/) (2025)
- [Informed Initialization for Bayesian Optimization and Active Learning](https://mlsanity.com/paper/2510.23681/) (2025)

## Abstract (arXiv)

Many engineering and scientific workflows rely on expensive black-box evaluations, requiring sequential decisions that must both improve task performance and reduce uncertainty. Bayesian optimization (BO) and Bayesian experimental design (BED) provide powerful but largely separate treatments of goal-directed optimization and information-seeking experimentation, leaving limited guidance for hybrid settings in which learning and optimization are intrinsically coupled. We propose Pragmatic Curiosity (PraC), a unified framework for hybrid learning and optimization via active inference. PraC evaluates candidate queries by trading information gain about a task-relevant latent symbol against an expected regret-based potential over outcomes. This formulation exposes three operational design choices: which latent quantity should be clarified, how task value is encoded as regret, and how strongly information gain should be exchanged against pragmatic value. We instantiate PraC across three regimes of increasing complexity: decision-oriented plume monitoring with fixed global symbols and known downstream losses, targeted active search with induced local symbols and evolving coverage goals, and composite Bayesian optimization with hierarchical regret learning under unknown preferences. Across these regimes, PraC reduces downstream decision risk, improves coverage of critical outcome regions, and jointly learns predictive and preference structures without relying on task-specific staging rules.