Bayesian quadrature optimization (BQO) maximizes the expectation of an
expensive black-box integrand taken over a known probability distribution. In
this work, we study BQO under distributional uncertainty in which the
underlying probability distribution is unknown except for a limited set of its
i.i.d. samples. A standard BQO approach maximizes the Monte Carlo estimate of
the true expected objective given the fixed sample set. Though Monte Carlo
estimate is unbiased, it has high variance given a small set of samples; thus
can result in a spurious objective function. We adopt the distributionally
robust optimization perspective to this problem by maximizing the expected
objective under the most adversarial distribution. In particular, we propose a
novel posterior sampling based algorithm, namely distributionally robust BQO
(DRBQO) for this purpose. We demonstrate the empirical effectiveness of our
proposed framework in synthetic and real-world problems, and characterize its
theoretical convergence via Bayesian regret.

本研究针对具有分布不确定性的贝叶斯积分优化问题使用分布鲁棒优化视角，提出了一种基于后验抽样的算法（DRBQO），旨在最大化最对抗分布下的预期目标，并通过贝叶斯遗憾度量其理论收敛性。我们在合成和真实世界问题中展示了我们提出的框架的实证有效性。