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.

本文介绍了一种新颖的稳健贝叶斯优化算法 AIRBO，它可以在任意输入不确定性下有效地识别表现稳定良好的稳健最优解。我们的方法通过在高斯过程中使用最大均值差异 (MMD)，直接建模任意分布的不确定输入，并通过 Nystrom 近似加速后验推理，从而在 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上进行了大量实验，证明了我们的方法可以处理各种输入不确定性并实现最先进的性能。