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

2026-02-05

AI Summary

This work addresses the theoretical underpinnings of the exploration–exploitation trade-off in active inference, where balancing curiosity and utility is essential for consistent learning and regret-minimized decision-making. By minimizing expected free energy (EFE), the authors unify information gain and task performance within a single framework and provide the first theoretical guarantees for EFE-minimizing agents: sufficient curiosity simultaneously ensures Bayesian posterior consistency and bounded cumulative regret. The study establishes a formal relationship between the intensity of curiosity and both learning consistency and optimization efficiency, thereby bridging active inference with Bayesian experimental design and Bayesian optimization. Empirical results validate the proposed tuning criterion for curiosity-driven exploration.

Technology Category

• Machine Learning: Active Learning
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Reasoning under Uncertainty: Probabilistic Inference

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

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.

Problem

• Active Inference
• Expected Free Energy
• Curiosity
• Bayesian Consistency
• No-Regret Optimization

Innovation

• Active Inference
• Expected Free Energy
• Bayesian Consistency
• No-Regret Optimization
• Curiosity-driven Exploration