Bayesian Optimization of Robustness Measures Using Randomized GP-UCB-based Algorithms under Input Uncertainty

• URL: http://arxiv.org/abs/2504.03172v1
• Date: Fri, 04 Apr 2025 05:01:54 GMT
• Title: Bayesian Optimization of Robustness Measures Using Randomized GP-UCB-based Algorithms under Input Uncertainty
• Authors: Yu Inatsu,
• Abstract summary: We propose a new method called randomized robustness measure GP-UCB (RRGP-UCB)<n>RRGP-UCB samples the trade-off parameter $beta$ from a probability distribution based on a chi-squared distribution and avoids explicitly specifying $beta$.<n>We show that RRGP-UCB provides tight bounds on the expected value of regret based on the optimal solution and estimated solutions.
• Score: 3.8979646385036175
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bayesian optimization based on Gaussian process upper confidence bound (GP-UCB) has a theoretical guarantee for optimizing black-box functions. Black-box functions often have input uncertainty, but even in this case, GP-UCB can be extended to optimize evaluation measures called robustness measures. However, GP-UCB-based methods for robustness measures include a trade-off parameter $\beta$, which must be excessively large to achieve theoretical validity, just like the original GP-UCB. In this study, we propose a new method called randomized robustness measure GP-UCB (RRGP-UCB), which samples the trade-off parameter $\beta$ from a probability distribution based on a chi-squared distribution and avoids explicitly specifying $\beta$. The expected value of $\beta$ is not excessively large. Furthermore, we show that RRGP-UCB provides tight bounds on the expected value of regret based on the optimal solution and estimated solutions. Finally, we demonstrate the usefulness of the proposed method through numerical experiments.

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