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Risk Seeking Bayesian Optimization under Uncertainty for Obtaining Extremum

Shogo Iwazaki · Tomohiko Tanabe · Mitsuru Irie · Shion Takeno · Yu Inatsu

MR1 & MR2 - Number 175
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Fri 3 May 8 a.m. PDT — 8:30 a.m. PDT


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.

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