Bayesian Optimization (BO) is a sample-efficient optimization algorithm widely employed across various applications. In some challenging BO tasks, input uncertainty arises due to the inevitable randomness in the optimization process, such as machining errors, execution noise, or contextual variability. This uncertainty deviates the input from the intended value before evaluation, resulting in significant performance fluctuations in the final result. In this paper, we introduce a novel robust Bayesian Optimization algorithm, AIRBO, which can effectively identify a robust optimum that performs consistently well under arbitrary input uncertainty. Our method directly models the uncertain inputs of arbitrary distributions by empowering the Gaussian Process with the Maximum Mean Discrepancy (MMD) and further accelerates the posterior inference via Nystrom approximation. Rigorous theoretical regret bound is established under MMD estimation error and extensive experiments on synthetic functions and real problems demonstrate that our approach can handle various input uncertainties and achieve state-of-the-art performance.

翻译：贝叶斯优化（BO）是一种样本高效的优化算法，广泛应用于各类任务中。在某些具有挑战性的BO任务中，由于优化过程中不可避免的随机性（如加工误差、执行噪声或上下文变异性），输入不确定性随之产生。这种不确定性会导致实际评估前的输入值偏离预期值，进而造成最终结果的显著性能波动。本文提出了一种新颖的鲁棒贝叶斯优化算法AIRBO，该算法能够有效识别在任意输入不确定性下均保持稳定性能的鲁棒最优解。我们的方法通过将高斯过程与最大均值差异（MMD）相结合，直接对任意分布的输入不确定性进行建模，并利用Nyström近似加速后验推理。在MMD估计误差下建立了严格的理论遗憾界，并在合成函数和实际问题的广泛实验中证明，该方法能够处理多种输入不确定性，达到最先进的性能水平。