Bayesian optimization with output-weighted optimal sampling

In Bayesian optimization, accounting for the importance of the output relative to the input is a crucial yet challenging exercise, as it can considerably improve the final result but often involves inaccurate and cumbersome entropy estimations. We approach the problem from the perspective of importance-sampling theory, and advocate the use of the likelihood ratio to guide the search algorithm towards regions of the input space where the objective function to minimize assumes abnormally small values. The likelihood ratio acts as a sampling weight and can be computed at each iteration without severely deteriorating the overall efficiency of the algorithm. In particular, it can be approximated in a way that makes the approach tractable in high dimensions. The likelihood-weighted acquisition functions introduced in this work are found to outperform their unweighted counterparts in a number of applications. (c) 2020 Elsevier Inc. All rights reserved.

Automated summary

In Bayesian optimization, considering the importance of the output relative to the input is crucial yet challenging. This paper proposes using the likelihood ratio to guide the search algorithm, leading to better performance in various applications. The likelihood-weighted acquisition functions introduced in this work outperform their unweighted counterparts in multiple scenarios.