<ul><li>Bayesian optimization based on Gaussian process upper confidence bound (GP-UCB) has a theoretical guarantee for optimizing black-box functions.</li><li>A new method called randomized robustness measure GP-UCB (RRGP-UCB) is proposed, which avoids explicitly specifying the trade-off parameter β in GP-UCB-based methods for robustness measures.</li><li>RRGP-UCB samples the trade-off parameter β from a probability distribution based on a chi-squared distribution, providing tight bounds on the expected value of regret.</li><li>The usefulness of RRGP-UCB is demonstrated through numerical experiments.</li></ul>

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

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