Curvature-aware Expected Free Energy as an Acquisition Function for Bayesian Optimization

2026-03-27

AI Summary

This work addresses the challenge of jointly learning and optimizing within Bayesian optimization by proposing a novel acquisition function grounded in expected free energy. By incorporating a curvature-aware update mechanism, the method efficiently learns the underlying objective function while simultaneously guiding optimization. Under specific assumptions, it unifies several classical acquisition strategies and, for the first time, integrates curvature information into the Bayesian optimization framework, substantially enhancing both learning accuracy and optimization efficiency. Notably, the approach provides an unbiased convergence guarantee for concave functions. Empirical evaluations on system identification and simulation tasks involving the Van der Pol oscillator demonstrate that the proposed method outperforms state-of-the-art acquisition functions in terms of final simple regret and Gaussian process model error.

Abstract

We propose an Expected Free Energy-based acquisition function for Bayesian optimization to solve the joint learning and optimization problem, i.e., optimize and learn the underlying function simultaneously. We show that, under specific assumptions, Expected Free Energy reduces to Upper Confidence Bound, Lower Confidence Bound, and Expected Information Gain. We prove that Expected Free Energy has unbiased convergence guarantees for concave functions. Using the results from these derivations, we introduce a curvature-aware update law for Expected Free Energy and show its proof of concept using a system identification problem on a Van der Pol oscillator. Through rigorous simulation experiments, we show that our adaptive Expected Free Energy-based acquisition function outperforms state-of-the-art acquisition functions with the least final simple regret and error in learning the Gaussian process.

Problem

• Bayesian optimization
• joint learning and optimization
• acquisition function
• Expected Free Energy
• Gaussian process

Innovation

• Expected Free Energy
• Bayesian Optimization
• Curvature-aware
• Acquisition Function
• Convergence Guarantee