On the role of Model Uncertainties in Bayesian Optimization

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 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.

arXiv comment14 pages, 4 figures, 2 tables

References in corpus (8)

• Practical Bayesian Optimization of Machine Learning Algorithms
• Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift
• Accurate Uncertainties for Deep Learning Using Calibrated Regression
• Bayesian Optimization is Superior to Random Search for Machine Learning Hyperparameter Tuning: Analysis of the Black-Box Optimization Challenge 2020
• On the Expressiveness of Approximate Inference in Bayesian Neural Networks
• Uncertainty Toolbox: an Open-Source Library for Assessing, Visualizing, and Improving Uncertainty Quantification
• A Stratified Analysis of Bayesian Optimization Methods
• Calibrated and Sharp Uncertainties in Deep Learning via Density Estimation