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

arXiv: https://arxiv.org/abs/2603.26339 · HTML: https://mlsanity.com/paper/2603.26339/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 15 references that are in the map.
- First posted on arXiv 27 Mar 2026.

## Builds on (most cited first, 7 of 7)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Bayesian Optimization with Gradients](https://mlsanity.com/paper/1703.04389/) (2017)
- [Time-Varying Gaussian Process Bandit Optimization](https://mlsanity.com/paper/1601.06650/) (2016)
- [Whence the Expected Free Energy?](https://mlsanity.com/paper/2004.08128/) (2020)
- [Learning-based Methods for Adaptive Informative Path Planning](https://mlsanity.com/paper/2404.06940/) (2024)
- [Exploiting gradients and Hessians in Bayesian optimization and Bayesian quadrature](https://mlsanity.com/paper/1704.00060/) (2017)
- [Performance-Driven Cascade Controller Tuning with Bayesian Optimization](https://mlsanity.com/paper/2007.12536/) (2020)

## Built on by (most cited first, 1 of 1)

- [Expected Free Energy-based Informative Path Planning for Robotic Mars Exploration](https://mlsanity.com/paper/2608.14466/) (2026)

## Abstract (arXiv)

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.