Distributionally Robust Bayesian Quadrature Optimization

被引:0
作者
Thanh Tang Nguyen [1 ]
Gupta, Sunil [1 ]
Ha, Huong [1 ]
Rana, Santu [1 ]
Venkatesh, Svetha [1 ]
机构
[1] Deakin Univ, Appl Artificial Intelligence Inst A2I2, Geelong, Vic, Australia
来源
INTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS, VOL 108 | 2020年 / 108卷
基金
澳大利亚研究理事会;
关键词
D O I
暂无
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
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.
引用
收藏
页码:1921 / 1930
页数:10
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