On the role of Model Uncertainties in Bayesian Optimization
This work addresses the role of model uncertainties in Bayesian optimization, providing insights for researchers and practitioners, but it is incremental as it builds on existing methods without introducing new paradigms.
The study investigated how uncertainty calibration affects Bayesian optimization performance, finding a positive association between calibration error and regret that disappears when controlling for model type, and showing that re-calibration generally does not improve regret.
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 compare them across both synthetic and real-world experiments. Our results confirm that Gaussian Processes are strong surrogate models and that they tend to outperform other popular 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 model in the analysis. We also studied the effect of re-calibration 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.