Robust Bayesian Optimisation with Unbounded Corruptions

Abdelhamid Ezzerg, Ilija Bogunovic, Jeremias Knoblauch
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:28528-28565, 2026.

Abstract

Bayesian Optimization is critically vulnerable to extreme outliers. Existing provably robust methods typically assume a bounded cumulative corruption budget, which makes them defenseless against even a single corruption of sufficient magnitude. To address this, we introduce a new adversary whose budget is only bounded in the frequency of corruptions, not in their magnitude. We then derive RCGP-UCB, an algorithm coupling the upper confidence bound (UCB) approach with a Robust Conjugate Gaussian Process (RCGP). We present stable and adaptive versions of RCGP-UCB, and prove that they achieve sublinear regret in the presence of up to $O(T^{1/4})$ and $O(T^{1/7})$ corruptions with possibly infinite magnitude. This robustness comes at near zero cost: without outliers, RCGP-UCB’s regret bounds match those of the standard GP-UCB algorithm.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-ezzerg26a, title = {Robust {B}ayesian Optimisation with Unbounded Corruptions}, author = {Ezzerg, Abdelhamid and Bogunovic, Ilija and Knoblauch, Jeremias}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {28528--28565}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/ezzerg26a/ezzerg26a.pdf}, url = {https://proceedings.mlr.press/v306/ezzerg26a.html}, abstract = {Bayesian Optimization is critically vulnerable to extreme outliers. Existing provably robust methods typically assume a bounded cumulative corruption budget, which makes them defenseless against even a single corruption of sufficient magnitude. To address this, we introduce a new adversary whose budget is only bounded in the frequency of corruptions, not in their magnitude. We then derive RCGP-UCB, an algorithm coupling the upper confidence bound (UCB) approach with a Robust Conjugate Gaussian Process (RCGP). We present stable and adaptive versions of RCGP-UCB, and prove that they achieve sublinear regret in the presence of up to $O(T^{1/4})$ and $O(T^{1/7})$ corruptions with possibly infinite magnitude. This robustness comes at near zero cost: without outliers, RCGP-UCB’s regret bounds match those of the standard GP-UCB algorithm.} }
Endnote
%0 Conference Paper %T Robust Bayesian Optimisation with Unbounded Corruptions %A Abdelhamid Ezzerg %A Ilija Bogunovic %A Jeremias Knoblauch %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-ezzerg26a %I PMLR %P 28528--28565 %U https://proceedings.mlr.press/v306/ezzerg26a.html %V 306 %X Bayesian Optimization is critically vulnerable to extreme outliers. Existing provably robust methods typically assume a bounded cumulative corruption budget, which makes them defenseless against even a single corruption of sufficient magnitude. To address this, we introduce a new adversary whose budget is only bounded in the frequency of corruptions, not in their magnitude. We then derive RCGP-UCB, an algorithm coupling the upper confidence bound (UCB) approach with a Robust Conjugate Gaussian Process (RCGP). We present stable and adaptive versions of RCGP-UCB, and prove that they achieve sublinear regret in the presence of up to $O(T^{1/4})$ and $O(T^{1/7})$ corruptions with possibly infinite magnitude. This robustness comes at near zero cost: without outliers, RCGP-UCB’s regret bounds match those of the standard GP-UCB algorithm.
APA
Ezzerg, A., Bogunovic, I. & Knoblauch, J.. (2026). Robust Bayesian Optimisation with Unbounded Corruptions. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:28528-28565 Available from https://proceedings.mlr.press/v306/ezzerg26a.html.

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