Bayesian Optimization with Output-Weighted Optimal Sampling

Abstract

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.

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• Multi-fidelity Bayesian Optimization: A Review
• Output-Weighted Sampling for Multi-Armed Bandits with Extreme Payoffs
• Optimal criteria and their asymptotic form for data selection in data-driven reduced-order modeling with Gaussian process regression
• Epsilon-Greedy Thompson Sampling to Bayesian Optimization
• On the performance of multi-fidelity and reduced-dimensional neural emulators for inference of physiological boundary conditions