Robust Satisficing Gaussian Process Bandits Under Adversarial Attacks

2025-06-02

AI Summary

Gaussian process (GP) optimization under unknown, time-varying adversarial perturbations poses significant robustness challenges. Existing approaches typically aim to maximize worst-case performance, which is overly conservative and impractical under persistent uncertainty. Method: This paper introduces “robust satisficing”—a novel paradigm that prioritizes reliably achieving a pre-specified performance threshold τ, rather than optimizing for the worst case. It is the first to integrate satisficing principles into adversarial GP bandits, establishing a unified framework accommodating both oblivious and adaptive adversaries, with rigorous theoretical guarantees. Contributions/Results: We derive two new regret bounds: (i) a conditional sublinear time-regret under mild assumptions, and (ii) a perturbation-dependent regret proportional to the cumulative perturbation magnitude—valid without any adversary assumptions. Experiments demonstrate that our method significantly outperforms existing robust GP optimization techniques, especially under misspecified perturbation uncertainty sets—a common practical scenario.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Search and Optimization: Adversarial Search
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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 $ au$, 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 $ au$, 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.

Problem

• Optimizing Gaussian Process under adversarial perturbations
• Achieving predefined performance threshold under adversarial conditions
• Outperforming robust optimization with inaccurate ambiguity sets

Innovation

• Robust satisficing Gaussian Process optimization
• Two novel algorithms with distinct guarantees
• Sublinear regret bounds under adversarial conditions