Robust Satisficing Gaussian Process Bandits Under Adversarial Attacks

TL;DR

This paper introduces robust satisficing algorithms for Gaussian Process bandits that maintain predefined performance levels under adversarial attacks, outperforming traditional robust optimization methods especially when model assumptions are inaccurate.

Contribution

The paper proposes two novel robust satisficing algorithms for GP bandits, providing new guarantees under adversarial conditions and broadening the scope of robust optimization.

Findings

Algorithms achieve sublinear regret under certain adversarial assumptions.

Performance is robust even when the ambiguity set is inaccurately specified.

Outperforms existing robust optimization methods in experiments.

Abstract

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 $\tau$, 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 $\tau$, 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.