Mean-Variance Analysis in Bayesian Optimization under Uncertainty
This work addresses decision-making under uncertainty for applications like finance and engineering, but it is incremental as it adapts existing mean-variance analysis to Bayesian optimization settings.
The paper tackles the problem of active learning in uncertain environments by introducing Mean-Variance Analysis in Bayesian Optimization (MVA-BO) to handle trade-offs between average and variance of uncertainty, and it shows effectiveness through theoretical analysis and numerical experiments.
We consider active learning (AL) in an uncertain environment in which trade-off between multiple risk measures need to be considered. As an AL problem in such an uncertain environment, we study Mean-Variance Analysis in Bayesian Optimization (MVA-BO) setting. Mean-variance analysis was developed in the field of financial engineering and has been used to make decisions that take into account the trade-off between the average and variance of investment uncertainty. In this paper, we specifically focus on BO setting with an uncertain component and consider multi-task, multi-objective, and constrained optimization scenarios for the mean-variance trade-off of the uncertain component. When the target blackbox function is modeled by Gaussian Process (GP), we derive the bounds of the two risk measures and propose AL algorithm for each of the above three problems based on the risk measure bounds. We show the effectiveness of the proposed AL algorithms through theoretical analysis and numerical experiments.