Bayesian Optimization of Robustness Measures under Input Uncertainty: A Randomized Gaussian Process Upper Confidence Bound Approach

• URL: http://arxiv.org/abs/2504.03172v2
• Date: Wed, 23 Jul 2025 07:15:01 GMT
• Title: Bayesian Optimization of Robustness Measures under Input Uncertainty: A Randomized Gaussian Process Upper Confidence Bound Approach
• Authors: Yu Inatsu,
• Abstract summary: Black-box functions often involve input uncertainty.<n>Black-box functions often involve input uncertainty.<n>RRGP-UCB is a novel method that samples $beta$ from a chi-squared-based probability distribution.
• Score: 3.8979646385036175
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bayesian optimization based on the Gaussian process upper confidence bound (GP-UCB) offers a theoretical guarantee for optimizing black-box functions. In practice, however, black-box functions often involve input uncertainty. To handle such cases, GP-UCB can be extended to optimize evaluation criteria known as robustness measures. However, GP-UCB-based methods for robustness measures require a trade-off parameter, $\beta$, which, as in the original GP-UCB, must be set sufficiently large to ensure theoretical validity. In this study, we propose randomized robustness measure GP-UCB (RRGP-UCB), a novel method that samples $\beta$ from a chi-squared-based probability distribution. This approach eliminates the need to explicitly specify $\beta$. Notably, the expected value of $\beta$ under this distribution is not excessively large. Furthermore, we show that RRGP-UCB provides tight bounds on the expected regret between the optimal and estimated solutions. Numerical experiments demonstrate the effectiveness of the proposed method.

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