This is the code for our AISTATS 2020 paper "Distributionally Robust Bayesian Quadrature Optimization".
Within the main directory drbqo, run:
python -m examples.run_drbqo_synthetic
-
Change
DRBQO_MAIN_DIRindrbqo/examples/cv/__init__.pyto the full path of your local drbqo main directory -
To run DRBQO for Elasticnet, within the main directory
drbqo, run:
python -m examples.cv.elasticnet.main
- To run DRBQO for CNN, within the main directory
drbqo, run:
python -m examples.cv.cnn.main
@InProceedings{pmlr-v108-nguyen20a,
title = {Distributionally Robust Bayesian Quadrature Optimization},
author = {Tang Nguyen, Thanh and Gupta, Sunil and Ha, Huong and Rana, Santu and Venkatesh, Svetha},
booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics},
pages = {1921--1931},
year = {2020},
editor = {Chiappa, Silvia and Calandra, Roberto},
volume = {108},
series = {Proceedings of Machine Learning Research},
address = {Online},
month = {26--28 Aug},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v108/nguyen20a/nguyen20a.pdf},
url = {http://proceedings.mlr.press/v108/nguyen20a.html},
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.}
}