Robust Satisficing Gaussian Process Bandits Under Adversarial Attacks
This addresses the challenge of reliable optimization in adversarial environments for applications like robotics or finance, though it is incremental as it builds on existing robust optimization frameworks.
The paper tackles the problem of Gaussian Process optimization under adversarial attacks by introducing a robust satisficing objective to consistently achieve a predefined performance threshold, and shows that their algorithms outperform existing robust optimization methods in experiments, with derived sublinear regret bounds under certain conditions.
We address the problem of Gaussian Process (GP) optimization in the presence of unknown and potentially varying adversarial perturbations. Unlike traditional robust optimization approaches that focus on maximizing performance under worst-case scenarios, we consider a robust satisficing objective, where the goal is to consistently achieve a predefined performance threshold $τ$, even under adversarial conditions. We propose two novel algorithms based on distinct formulations of robust satisficing, and show that they are instances of a general robust satisficing framework. Further, each algorithm offers different guarantees depending on the nature of the adversary. Specifically, we derive two regret bounds: one that is sublinear over time, assuming certain conditions on the adversary and the satisficing threshold $τ$, and another that scales with the perturbation magnitude but requires no assumptions on the adversary. Through extensive experiments, we demonstrate that our approach outperforms the established robust optimization methods in achieving the satisficing objective, particularly when the ambiguity set of the robust optimization framework is inaccurately specified.