# Robust Bayesian Optimisation with Unbounded Corruptions

arXiv: https://arxiv.org/abs/2511.15315 · HTML: https://mlsanity.com/paper/2511.15315/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 56 references that are in the map.
- First posted on arXiv 19 Nov 2025.

## Builds on (most cited first, 30 of 31)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [SMAC3: A Versatile Bayesian Optimization Package for Hyperparameter Optimization](https://mlsanity.com/paper/2109.09831/) (2021)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Stochastic bandits robust to adversarial corruptions](https://mlsanity.com/paper/1803.09353/) (2018)
- [Better Algorithms for Stochastic Bandits with Adversarial Corruptions](https://mlsanity.com/paper/1902.08647/) (2019)
- [Adversarially Robust Optimization with Gaussian Processes](https://mlsanity.com/paper/1810.10775/) (2018)
- [Automated Machine Learning: From Principles to Practices](https://mlsanity.com/paper/1810.13306/) (2018)
- [Generalized Variational Inference: Three arguments for deriving new Posteriors](https://mlsanity.com/paper/1904.02063/) (2019)
- [Misspecified Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2111.05008/) (2021)
- [Robust Generalised Bayesian Inference for Intractable Likelihoods](https://mlsanity.com/paper/2104.07359/) (2021)
- [Student-t Processes as Alternatives to Gaussian Processes](https://mlsanity.com/paper/1402.4306/) (2014)
- [Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap](https://mlsanity.com/paper/2202.04744/) (2022)
- [Corruption-Tolerant Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2003.01971/) (2020)
- [A Rigorous Link between Deep Ensembles and (Variational) Bayesian Methods](https://mlsanity.com/paper/2305.15027/) (2023)
- [Regret bounds for meta Bayesian optimization with an unknown Gaussian process prior](https://mlsanity.com/paper/1811.09558/) (2018)
- [Practical Bayesian optimization in the presence of outliers](https://mlsanity.com/paper/1712.04567/) (2017)
- [Doubly Robust Bayesian Inference for Non-Stationary Streaming Data with β-Divergences](https://mlsanity.com/paper/1806.02261/) (2018)
- [Outlier-robust Kalman Filtering through Generalised Bayes](https://mlsanity.com/paper/2405.05646/) (2024)
- [Byzantine-Tolerant Machine Learning](https://mlsanity.com/paper/1703.02757/) (2017)
- [Generalized Posteriors in Approximate Bayesian Computation](https://mlsanity.com/paper/2011.08644/) (2020)
- [Generalised Bayesian Inference for Discrete Intractable Likelihood](https://mlsanity.com/paper/2206.08420/) (2022)
- [Robust and Conjugate Gaussian Process Regression](https://mlsanity.com/paper/2311.00463/) (2023)
- [Bias-Robust Bayesian Optimization via Dueling Bandits](https://mlsanity.com/paper/2105.11802/) (2021)
- [A Robust Phased Elimination Algorithm for Corruption-Tolerant Gaussian Process Bandits](https://mlsanity.com/paper/2202.01850/) (2022)
- [Robust and Conjugate Spatio-Temporal Gaussian Processes](https://mlsanity.com/paper/2502.02450/) (2025)
- [Prediction-Centric Uncertainty Quantification via MMD](https://mlsanity.com/paper/2410.11637/) (2024)
- [Robust expected improvement for Bayesian optimization](https://mlsanity.com/paper/2302.08612/) (2023)
- [Active learning for affinity prediction of antibodies](https://mlsanity.com/paper/2406.07263/) (2024)

## Built on by (most cited first, 1 of 1)

- [Sharper Guarantees for Misspecified Kernelized Bandit Optimization](https://mlsanity.com/paper/2605.05967/) (2026)

## Abstract (arXiv)

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 famous 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(T1/4) and O(T1/7) 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.