Bayesian optimisation under uncertain inputs

Rafael Oliveira, Lionel Ott, Fabio Ramos
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:1177-1184, 2019.

Abstract

Bayesian optimisation (BO) has been a successful approach to optimise functions which are expensive to evaluate and whose observations are noisy. Classical BO algorithms, however, do not account for errors about the location where observations are taken, which is a common issue in problems with physical components. In these cases, the estimation of the actual query location is also subject to uncertainty. In this context, we propose an upper confidence bound (UCB) algorithm for BO problems where both the outcome of a query and the true query location are uncertain. The algorithm employs a Gaussian process model that takes probability distributions as inputs. Theoretical results are provided for both the proposed algorithm and a conventional UCB approach within the uncertain-inputs setting. Finally, we evaluate each method’s performance experimentally, comparing them to other input noise aware BO approaches on simulated scenarios involving synthetic and real data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-oliveira19a, title = {Bayesian optimisation under uncertain inputs}, author = {Oliveira, Rafael and Ott, Lionel and Ramos, Fabio}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {1177--1184}, year = {2019}, editor = {Chaudhuri, Kamalika and Sugiyama, Masashi}, volume = {89}, series = {Proceedings of Machine Learning Research}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v89/oliveira19a/oliveira19a.pdf}, url = {https://proceedings.mlr.press/v89/oliveira19a.html}, abstract = {Bayesian optimisation (BO) has been a successful approach to optimise functions which are expensive to evaluate and whose observations are noisy. Classical BO algorithms, however, do not account for errors about the location where observations are taken, which is a common issue in problems with physical components. In these cases, the estimation of the actual query location is also subject to uncertainty. In this context, we propose an upper confidence bound (UCB) algorithm for BO problems where both the outcome of a query and the true query location are uncertain. The algorithm employs a Gaussian process model that takes probability distributions as inputs. Theoretical results are provided for both the proposed algorithm and a conventional UCB approach within the uncertain-inputs setting. Finally, we evaluate each method’s performance experimentally, comparing them to other input noise aware BO approaches on simulated scenarios involving synthetic and real data.} }
Endnote
%0 Conference Paper %T Bayesian optimisation under uncertain inputs %A Rafael Oliveira %A Lionel Ott %A Fabio Ramos %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-oliveira19a %I PMLR %P 1177--1184 %U https://proceedings.mlr.press/v89/oliveira19a.html %V 89 %X Bayesian optimisation (BO) has been a successful approach to optimise functions which are expensive to evaluate and whose observations are noisy. Classical BO algorithms, however, do not account for errors about the location where observations are taken, which is a common issue in problems with physical components. In these cases, the estimation of the actual query location is also subject to uncertainty. In this context, we propose an upper confidence bound (UCB) algorithm for BO problems where both the outcome of a query and the true query location are uncertain. The algorithm employs a Gaussian process model that takes probability distributions as inputs. Theoretical results are provided for both the proposed algorithm and a conventional UCB approach within the uncertain-inputs setting. Finally, we evaluate each method’s performance experimentally, comparing them to other input noise aware BO approaches on simulated scenarios involving synthetic and real data.
APA
Oliveira, R., Ott, L. & Ramos, F.. (2019). Bayesian optimisation under uncertain inputs. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:1177-1184 Available from https://proceedings.mlr.press/v89/oliveira19a.html.

Related Material