Bayesian Optimization of Robustness Measures under Input Uncertainty: A Randomized Gaussian Process Upper Confidence Bound Approach
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918102370877440 |
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| author | Inatsu, Yu |
| author_facet | Inatsu, Yu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03172 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bayesian Optimization of Robustness Measures under Input Uncertainty: A Randomized Gaussian Process Upper Confidence Bound Approach Inatsu, Yu Machine Learning 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. |
| title | Bayesian Optimization of Robustness Measures under Input Uncertainty: A Randomized Gaussian Process Upper Confidence Bound Approach |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2504.03172 |