Analysis of gradient-aware complex acquisition functions

Analyze how complex Bayesian Optimization for Simulator Inverse Problems acquisition functions, beyond MaxVar, should be adapted to gradient-enhanced Gaussian-process surrogates by marginalizing over the modeled simulator-output gradients.

Background

The paper extends the Bayesian Optimization for Simulator Inverse Problems (BOSIP) framework by conditioning Gaussian-process surrogates on both simulator-proxy function values and their parameter gradients. For the MaxVar acquisition function, the required posterior variance can be obtained from the marginal predictive distribution of the proxy variable, because the joint predictive distribution over proxy values and gradients is Gaussian.

For more complex acquisition functions, however, the acquisition calculation must account for the gradient components in the augmented predictive distribution. The paper states that this requires marginalization over the gradients but does not carry out that analysis; the experiments therefore use only MaxVar. Developing this extension would broaden the applicability of gradient-enhanced BOSIP to more sophisticated acquisition strategies.

References

In case of the more complex acquisition functions, such as the ones discussed in and , the adaptation is more involved, as we need to marginalize over the gradients. We leave the analysis of more complex acquisition functions for future work, as we only benchmark using the MaxVar acquisition in this study.

— Exploiting Gradients in Bayesian Inference of Expensive Simulators  (2610.12076 - Soldát et al., 8 Oct 2026) in Section 2, “Incorporating Gradient Information”