Bayesian Optimization with Output-Weighted Optimal Sampling
This work addresses a challenge in Bayesian optimization for researchers and practitioners, offering a tractable method for high-dimensional problems, but it appears incremental as it builds on existing importance-sampling theory.
The paper tackled the problem of improving Bayesian optimization by accounting for output importance relative to input, using a likelihood ratio to guide sampling toward regions with small objective function values, resulting in new acquisition functions that outperform unweighted ones in various applications.
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 be minimized 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.