aiqbench analysis
This research introduces a curvature-aware Expected Free Energy acquisition function for Bayesian optimization, offering unbiased convergence guarantees for concave functions and improved performance on oscillatory landscapes. By unifying learning and optimization under specific assumptions, the method reduces to established bounds like Upper Confidence Bound while addressing limitations in balancing regret and mean squared error. The study validates its approach through system identification on a Van der Pol oscillator, demonstrating competitive results in complex benchmark scenarios.
Curvature-aware Expected Free Energy as an Acquisition Function for Bayesian Optimization
arXiv:2603.26339v2 Announce Type: replace-cross 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. On a two-dimensional benchmark with an oscillatory landscape, our adaptive Expected Free Energy acquisition achieves competitive performance in both regret and mean squared error, unlike the typical acquisition functions that perform well in only one metric.
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. On a two-dimensional benchmark with an oscillatory landscape, our adaptive Expected Free Energy acquisition achieves competitive performance in both regret and mean squared error, unlike the typical acquisition functions that perform well in only one metric.
Machine Learning (cs.LG); Robotics (cs.RO); Systems and Control (eess.SY)
arXiv:2603.26339 [cs.LG]
(or arXiv:2603.26339v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2603.26339 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 228 words
