Bayesian Optimization for Distributionally Robust Chance-constrained Problem

Yu Inatsu, Shion Takeno, Masayuki Karasuyama, Ichiro Takeuchi
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:9602-9621, 2022.

Abstract

In black-box function optimization, we need to consider not only controllable design variables but also uncontrollable stochastic environment variables. In such cases, it is necessary to solve the optimization problem by taking into account the uncertainty of the environmental variables. Chance-constrained (CC) problem, the problem of maximizing the expected value under a certain level of constraint satisfaction probability, is one of the practically important problems in the presence of environmental variables. In this study, we consider distributionally robust CC (DRCC) problem and propose a novel DRCC Bayesian optimization method for the case where the distribution of the environmental variables cannot be precisely specified. We show that the proposed method can find an arbitrary accurate solution with high probability in a finite number of trials, and confirm the usefulness of the proposed method through numerical experiments.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-inatsu22a, title = {{B}ayesian Optimization for Distributionally Robust Chance-constrained Problem}, author = {Inatsu, Yu and Takeno, Shion and Karasuyama, Masayuki and Takeuchi, Ichiro}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {9602--9621}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/inatsu22a/inatsu22a.pdf}, url = {https://proceedings.mlr.press/v162/inatsu22a.html}, abstract = {In black-box function optimization, we need to consider not only controllable design variables but also uncontrollable stochastic environment variables. In such cases, it is necessary to solve the optimization problem by taking into account the uncertainty of the environmental variables. Chance-constrained (CC) problem, the problem of maximizing the expected value under a certain level of constraint satisfaction probability, is one of the practically important problems in the presence of environmental variables. In this study, we consider distributionally robust CC (DRCC) problem and propose a novel DRCC Bayesian optimization method for the case where the distribution of the environmental variables cannot be precisely specified. We show that the proposed method can find an arbitrary accurate solution with high probability in a finite number of trials, and confirm the usefulness of the proposed method through numerical experiments.} }
Endnote
%0 Conference Paper %T Bayesian Optimization for Distributionally Robust Chance-constrained Problem %A Yu Inatsu %A Shion Takeno %A Masayuki Karasuyama %A Ichiro Takeuchi %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-inatsu22a %I PMLR %P 9602--9621 %U https://proceedings.mlr.press/v162/inatsu22a.html %V 162 %X In black-box function optimization, we need to consider not only controllable design variables but also uncontrollable stochastic environment variables. In such cases, it is necessary to solve the optimization problem by taking into account the uncertainty of the environmental variables. Chance-constrained (CC) problem, the problem of maximizing the expected value under a certain level of constraint satisfaction probability, is one of the practically important problems in the presence of environmental variables. In this study, we consider distributionally robust CC (DRCC) problem and propose a novel DRCC Bayesian optimization method for the case where the distribution of the environmental variables cannot be precisely specified. We show that the proposed method can find an arbitrary accurate solution with high probability in a finite number of trials, and confirm the usefulness of the proposed method through numerical experiments.
APA
Inatsu, Y., Takeno, S., Karasuyama, M. & Takeuchi, I.. (2022). Bayesian Optimization for Distributionally Robust Chance-constrained Problem. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:9602-9621 Available from https://proceedings.mlr.press/v162/inatsu22a.html.

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