Wasserstein Distributionally Robust Bayesian Optimization with Continuous Context

Francesco Micheli, Efe C. Balta, Anastasios Tsiamis, John Lygeros
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:4978-4986, 2025.

Abstract

We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of uncontrollable contextual variables. We consider the setting where the context distribution is uncertain but known to lie within an ambiguity set defined as a ball in the Wasserstein distance. We propose a novel algorithm for Wasserstein Distributionally Robust Bayesian Optimization that can handle continuous context distributions while maintaining computational tractability. Our theoretical analysis combines recent results in self-normalized concentration in Hilbert spaces and finite-sample bounds for distributionally robust optimization to establish sublinear regret bounds that match state-of-the-art results. Through extensive comparisons with existing approaches on both synthetic and real-world problems, we demonstrate the simplicity, effectiveness, and practical applicability of our proposed method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-micheli25a, title = {Wasserstein Distributionally Robust Bayesian Optimization with Continuous Context}, author = {Micheli, Francesco and Balta, Efe C. and Tsiamis, Anastasios and Lygeros, John}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {4978--4986}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/micheli25a/micheli25a.pdf}, url = {https://proceedings.mlr.press/v258/micheli25a.html}, abstract = {We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of uncontrollable contextual variables. We consider the setting where the context distribution is uncertain but known to lie within an ambiguity set defined as a ball in the Wasserstein distance. We propose a novel algorithm for Wasserstein Distributionally Robust Bayesian Optimization that can handle continuous context distributions while maintaining computational tractability. Our theoretical analysis combines recent results in self-normalized concentration in Hilbert spaces and finite-sample bounds for distributionally robust optimization to establish sublinear regret bounds that match state-of-the-art results. Through extensive comparisons with existing approaches on both synthetic and real-world problems, we demonstrate the simplicity, effectiveness, and practical applicability of our proposed method.} }
Endnote
%0 Conference Paper %T Wasserstein Distributionally Robust Bayesian Optimization with Continuous Context %A Francesco Micheli %A Efe C. Balta %A Anastasios Tsiamis %A John Lygeros %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-micheli25a %I PMLR %P 4978--4986 %U https://proceedings.mlr.press/v258/micheli25a.html %V 258 %X We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of uncontrollable contextual variables. We consider the setting where the context distribution is uncertain but known to lie within an ambiguity set defined as a ball in the Wasserstein distance. We propose a novel algorithm for Wasserstein Distributionally Robust Bayesian Optimization that can handle continuous context distributions while maintaining computational tractability. Our theoretical analysis combines recent results in self-normalized concentration in Hilbert spaces and finite-sample bounds for distributionally robust optimization to establish sublinear regret bounds that match state-of-the-art results. Through extensive comparisons with existing approaches on both synthetic and real-world problems, we demonstrate the simplicity, effectiveness, and practical applicability of our proposed method.
APA
Micheli, F., Balta, E.C., Tsiamis, A. & Lygeros, J.. (2025). Wasserstein Distributionally Robust Bayesian Optimization with Continuous Context. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:4978-4986 Available from https://proceedings.mlr.press/v258/micheli25a.html.

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