Curiosity is Knowledge: Self-Consistent Learning and No-Regret Optimization with Active Inference
This provides theoretical guarantees for active inference agents, connecting it to classical Bayesian methods and offering practical guidelines for tuning exploration-exploitation trade-offs in hybrid learning-optimization problems.
The paper tackled the problem of balancing exploration and exploitation in active inference by analyzing the Expected Free Energy (EFE) with a curiosity coefficient, establishing that sufficient curiosity ensures both self-consistent learning (Bayesian posterior consistency) and no-regret optimization (bounded cumulative regret).
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.