# Curiosity is Knowledge: Self-Consistent Learning and No-Regret Optimization with Active Inference

arXiv: https://arxiv.org/abs/2602.06029 · HTML: https://mlsanity.com/paper/2602.06029/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 22 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Builds on (most cited first, 8 of 8)

- [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)
- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [Maximizing acquisition functions for Bayesian optimization](https://mlsanity.com/paper/1805.10196/) (2018)
- [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)
- [On the Implementation of a Bayesian Optimization Framework for Interconnected Systems](https://mlsanity.com/paper/2501.00967/) (2025)

## Abstract (arXiv)

Active inference (AIF) unifies exploration and exploitation by minimizing the Expected Free Energy (EFE), balancing epistemic value (information gain) and pragmatic value (task performance) through a curiosity coefficient. Yet it has been unclear when this balance yields both coherent learning and efficient decision-making: insufficient curiosity can drive myopic exploitation and prevent uncertainty resolution, while excessive curiosity can induce unnecessary exploration and regret. We establish the first theoretical guarantee for EFE-minimizing agents, showing that a single requirement--sufficient curiosity--simultaneously ensures self-consistent learning (Bayesian posterior consistency) and no-regret optimization (bounded cumulative regret). Our analysis characterizes how this mechanism depends on initial uncertainty, identifiability, and objective alignment, thereby connecting AIF to classical Bayesian experimental design and Bayesian optimization within one theoretical framework. We further translate these theories into practical design guidelines for tuning the epistemic-pragmatic trade-off in hybrid learning-optimization problems, validated through real-world experiments.