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

TL;DR

This paper provides a theoretical guarantee that sufficient curiosity in active inference ensures both consistent learning and no-regret decision-making, connecting exploration-exploitation balance with classical Bayesian methods.

Contribution

It establishes the first theoretical guarantee linking curiosity levels in active inference to both learning consistency and regret minimization, with practical guidelines.

Findings

Sufficient curiosity guarantees Bayesian posterior consistency.

Sufficient curiosity ensures bounded cumulative regret.

Theoretical insights connect active inference with Bayesian optimization.

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.