Mean-Variance Analysis in Bayesian Optimization under Uncertainty

Shogo Iwazaki, Yu Inatsu, Ichiro Takeuchi
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:973-981, 2021.

Abstract

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 scenarios based on the risk measure bounds. We show the effectiveness of the proposed AL algorithms through theoretical analysis and numerical experiments.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-iwazaki21a, title = { Mean-Variance Analysis in Bayesian Optimization under Uncertainty }, author = {Iwazaki, Shogo and Inatsu, Yu and Takeuchi, Ichiro}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {973--981}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/iwazaki21a/iwazaki21a.pdf}, url = {https://proceedings.mlr.press/v130/iwazaki21a.html}, abstract = { 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 scenarios based on the risk measure bounds. We show the effectiveness of the proposed AL algorithms through theoretical analysis and numerical experiments. } }
Endnote
%0 Conference Paper %T Mean-Variance Analysis in Bayesian Optimization under Uncertainty %A Shogo Iwazaki %A Yu Inatsu %A Ichiro Takeuchi %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-iwazaki21a %I PMLR %P 973--981 %U https://proceedings.mlr.press/v130/iwazaki21a.html %V 130 %X 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 scenarios based on the risk measure bounds. We show the effectiveness of the proposed AL algorithms through theoretical analysis and numerical experiments.
APA
Iwazaki, S., Inatsu, Y. & Takeuchi, I.. (2021). Mean-Variance Analysis in Bayesian Optimization under Uncertainty . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:973-981 Available from https://proceedings.mlr.press/v130/iwazaki21a.html.

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