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

arXiv: https://arxiv.org/abs/2504.03172 · HTML: https://mlsanity.com/paper/2504.03172/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2025.

## Abstract (arXiv)

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, β, 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 β from a chi-squared-based probability distribution. This approach eliminates the need to explicitly specify β. Notably, the expected value of β 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.