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Bayesian Optimization (BO) is a sample-efficient optimization algorithmwidely employed across various applications. In some challenging BO tasks,input uncertainty arises due to the inevitable randomness in the optimizationprocess, 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 thispaper, we introduce a novel robust Bayesian Optimization algorithm, AIRBO,which can effectively identify a robust optimum that performs consistently wellunder arbitrary input uncertainty. Our method directly models the uncertaininputs of arbitrary distributions by empowering the Gaussian Process with theMaximum Mean Discrepancy (MMD) and further accelerates the posterior inferencevia Nystrom approximation. Rigorous theoretical regret bound is establishedunder MMD estimation error and extensive experiments on synthetic functions andreal problems demonstrate that our approach can handle various inputuncertainties and achieve state-of-the-art performance.

Efficient Robust Bayesian Optimization for Arbitrary Uncertain Inputs