新算法在极端异常值下仍能稳定优化，且无需限制异常值大小。
Robust Bayesian Optimisation with Unbounded Corruptions
- 设计新型对抗模型：只限制异常发生频率，不限制其强度。
- 可应对最多 $O(T^{1/4})$ 次任意强度异常，仍保持亚线性损失。
- 与标准方法相比，无异常时性能几乎无损，适合高可靠性场景。
贝叶斯优化对极端异常值极为敏感。现有可证明鲁棒的方法通常假设累计污染预算有界，导致对单个极大异常毫无防御能力。为此，我们提出一种新对抗模型，其预算仅在异常发生频率上受限，不限制异常幅度。基于此，我们推导出 RCGP-UCB 算法，将经典的上置信界（UCB）策略与鲁棒共轭高斯过程（RCGP）结合。我们提出了稳定和自适应版本的 RCGP-UCB，证明其在存在最多 $O(T^{1/4})$ 和 $O(T^{1/7})$ 次可能无限幅度的异常时，仍能实现亚线性后悔。这种鲁棒性几乎不增加成本：在无异常情况下，其后悔界与标准 GP-UCB 完全一致。
原文摘要 · Abstract (English)
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 $O(T^{1/4})$ 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.
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