Unbounded Bayesian Optimization via Regularization
Bobak Shahriari, Alexandre Bouchard-Cote, Nando Freitas
Abstract
Bayesian optimization has recently emerged as a powerful and flexible tool in machine learning for hyperparameter tuning and more generally for the efficient global optimization of expensive black box functions. The established practice requires a user-defined bounded domain, which is assumed to contain the global optimizer. However, when little is known about the probed objective function, it can be difficult to prescribe such a domain. In this work, we modify the standard Bayesian optimization framework in a principled way to allow for unconstrained exploration of the search space. We introduce a new alternative method and compare it to a volume doubling baseline on two common synthetic benchmarking test functions. Finally, we apply our proposed methods on the task of tuning the stochastic gradient descent optimizer for both a multi-layered perceptron and a convolutional neural network on the MNIST dataset.
BibTeX
@InProceedings{pmlr-v51-shahriari16,
title = {Unbounded Bayesian Optimization via Regularization},
author = {Shahriari, Bobak and Bouchard-Cote, Alexandre and Freitas, Nando},
booktitle = {Proceedings of the 19th International Conference on Artificial Intelligence and Statistics},
pages = {1168--1176},
year = {2016},
editor = {Gretton, Arthur and Robert, Christian C.},
volume = {51},
series = {Proceedings of Machine Learning Research},
address = {Cadiz, Spain},
month = {09--11 May},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v51/shahriari16.pdf},
url = {https://proceedings.mlr.press/v51/shahriari16.html},
abstract = {Bayesian optimization has recently emerged as a powerful and flexible tool in machine learning for hyperparameter tuning and more generally for the efficient global optimization of expensive black box functions. The established practice requires a user-defined bounded domain, which is assumed to contain the global optimizer. However, when little is known about the probed objective function, it can be difficult to prescribe such a domain. In this work, we modify the standard Bayesian optimization framework in a principled way to allow for unconstrained exploration of the search space. We introduce a new alternative method and compare it to a volume doubling baseline on two common synthetic benchmarking test functions. Finally, we apply our proposed methods on the task of tuning the stochastic gradient descent optimizer for both a multi-layered perceptron and a convolutional neural network on the MNIST dataset.}
}