%0 Journal Article %1 nguyen2020distributionally %A Nguyen, Thanh Tang %A Gupta, Sunil %A Ha, Huong %A Rana, Santu %A Venkatesh, Svetha %D 2020 %K bayesian optimization readings robustness %T Distributionally Robust Bayesian Quadrature Optimization %U http://arxiv.org/abs/2001.06814 %X 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.

@article{nguyen2020distributionally, abstract = {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.}, added-at = {2020-06-09T19:14:14.000+0200}, author = {Nguyen, Thanh Tang and Gupta, Sunil and Ha, Huong and Rana, Santu and Venkatesh, Svetha}, biburl = {https://www.bibsonomy.org/bibtex/23416eebce636e76acbb008d8dbe12f05/kirk86}, description = {[2001.06814] Distributionally Robust Bayesian Quadrature Optimization}, interhash = {2fcb7e7cf27b4d6bc1ae10c97a92838f}, intrahash = {3416eebce636e76acbb008d8dbe12f05}, keywords = {bayesian optimization readings robustness}, note = {cite arxiv:2001.06814Comment: AISTATS2020}, timestamp = {2020-06-09T19:14:44.000+0200}, title = {Distributionally Robust Bayesian Quadrature Optimization}, url = {http://arxiv.org/abs/2001.06814}, year = 2020 }