Robust Bayesian Optimisation with Unbounded Corruptions
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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.
Key facts. Cited by 1 paper 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
31 of 56 references.
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19 more
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