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

TL;DR

This paper introduces a curvature-aware Expected Free Energy acquisition function for Bayesian optimization, improving joint learning and optimization with theoretical guarantees and superior empirical performance.

Contribution

It develops a novel curvature-aware Expected Free Energy acquisition function with convergence guarantees, outperforming existing methods in experiments.

Findings

Outperforms state-of-the-art acquisition functions in simple regret and learning error.

Provides convergence guarantees for the proposed acquisition function.

Demonstrates effectiveness on a Van der Pol oscillator system identification.

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.