Risk Seeking Bayesian Optimization under Uncertainty for Obtaining Extremum
Shogo Iwazaki, Tomohiko Tanabe, Mitsuru Irie, Shion Takeno, Yu Inatsu
Abstract
Real-world black-box optimization tasks often focus on obtaining the best reward, which includes an intrinsic random quantity from uncontrollable environmental factors. For this problem, we formulate a novel risk-seeking optimization problem whose aim is to obtain the best possible reward within a fixed budget under uncontrollable factors. We consider two settings: (1) environmental model setting for the case that we can observe uncontrollable environmental variables that affect the observation as the input of a target function, and (2) heteroscedastic model setting for the case that any uncontrollable variables cannot be observed. We propose a novel Bayesian optimization method called kernel explore-then-commit (kernel-ETC) and provide the regret upper bound for both settings. We demonstrate the effectiveness of kernel-ETC through several numerical experiments, including the hyperparameter tuning task and the simulation function derived from polymer synthesis real data.
BibTeX
@InProceedings{pmlr-v238-iwazaki24a,
title = {Risk Seeking {B}ayesian Optimization under Uncertainty for Obtaining Extremum},
author = {Iwazaki, Shogo and Tanabe, Tomohiko and Irie, Mitsuru and Takeno, Shion and Inatsu, Yu},
booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics},
pages = {1252--1260},
year = {2024},
editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen},
volume = {238},
series = {Proceedings of Machine Learning Research},
month = {02--04 May},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v238/iwazaki24a/iwazaki24a.pdf},
url = {https://proceedings.mlr.press/v238/iwazaki24a.html},
abstract = {Real-world black-box optimization tasks often focus on obtaining the best reward, which includes an intrinsic random quantity from uncontrollable environmental factors. For this problem, we formulate a novel risk-seeking optimization problem whose aim is to obtain the best possible reward within a fixed budget under uncontrollable factors. We consider two settings: (1) environmental model setting for the case that we can observe uncontrollable environmental variables that affect the observation as the input of a target function, and (2) heteroscedastic model setting for the case that any uncontrollable variables cannot be observed. We propose a novel Bayesian optimization method called kernel explore-then-commit (kernel-ETC) and provide the regret upper bound for both settings. We demonstrate the effectiveness of kernel-ETC through several numerical experiments, including the hyperparameter tuning task and the simulation function derived from polymer synthesis real data.}
}