On the Role of Model Uncertainties in Bayesian Optimisation

Jonathan Foldager, Mikkel Jordahn, Lars Kai Hansen, Michael Riis Andersen

Keywords: Bayesian Optimisation, Calibration

Abstract: Bayesian Optimization (BO) is a popular method for black-box optimization, which relies on uncertainty as part of its decision-making process when deciding which experiment to perform next. However, not much work has addressed the effect of uncertainty on the performance of the BO algorithm and to what extent calibrated uncertainties improve the ability to find the global optimum. In this work, we provide an extensive study of the relationship between the BO performance (regret) and uncertainty calibration for popular surrogate models and acquisition functions, and compare them across both synthetic and real-world experiments. Our results show that Gaussian Processes, and more surprisingly, Deep Ensembles are strong surrogate models. Our results further show a positive association between calibration error and regret, but interestingly, this association disappears when we control for the type of surrogate model in the analysis. We also study the effect of recalibration and demonstrate that it generally does not lead to improved regret. Finally, we provide theoretical justification for why uncertainty calibration might be difficult to combine with BO due to the small sample sizes commonly used.