# Robust Satisficing Gaussian Process Bandits Under Adversarial Attacks

arXiv: https://arxiv.org/abs/2506.01625 · HTML: https://mlsanity.com/paper/2506.01625/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 43 references that are in the map.
- First posted on arXiv 2 Jun 2025.

## Builds on (most cited first, 24 of 24)

- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [Towards Deep Neural Network Architectures Robust to Adversarial Examples](https://mlsanity.com/paper/1412.5068/) (2014)
- [Adversarially Robust Optimization with Gaussian Processes](https://mlsanity.com/paper/1810.10775/) (2018)
- [Distributionally Robust Bayesian Optimization](https://mlsanity.com/paper/2002.09038/) (2020)
- [Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression](https://mlsanity.com/paper/2105.02796/) (2021)
- [Satisficing in Time-Sensitive Bandit Learning](https://mlsanity.com/paper/1803.02855/) (2018)
- [Virtual vs. Real: Trading Off Simulations and Physical Experiments in Reinforcement Learning with Bayesian Optimization](https://mlsanity.com/paper/1703.01250/) (2017)
- [Corruption-Tolerant Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2003.01971/) (2020)
- [Automatic LQR Tuning Based on Gaussian Process Global Optimization](https://mlsanity.com/paper/1605.01950/) (2016)
- [Practical Bayesian optimization in the presence of outliers](https://mlsanity.com/paper/1712.04567/) (2017)
- [Noisy-Input Entropy Search for Efficient Robust Bayesian Optimization](https://mlsanity.com/paper/2002.02820/) (2020)
- [AutoPrognosis: Automated Clinical Prognostic Modeling via Bayesian Optimization with Structured Kernel Learning](https://mlsanity.com/paper/1802.07207/) (2018)
- [Value-at-Risk Optimization with Gaussian Processes](https://mlsanity.com/paper/2105.06126/) (2021)
- [Bayesian optimisation under uncertain inputs](https://mlsanity.com/paper/1902.07908/) (2019)
- [Mean-Variance Analysis in Bayesian Optimization under Uncertainty](https://mlsanity.com/paper/2009.08166/) (2020)
- [Lenient Regret and Good-Action Identification in Gaussian Process Bandits](https://mlsanity.com/paper/2102.05793/) (2021)
- [A Robust Phased Elimination Algorithm for Corruption-Tolerant Gaussian Process Bandits](https://mlsanity.com/paper/2202.01850/) (2022)
- [Satisficing in multi-armed bandit problems](https://mlsanity.com/paper/1512.07638/) (2015)
- [Lenient Regret for Multi-Armed Bandits](https://mlsanity.com/paper/2008.03959/) (2020)
- [Robust Bayesian Satisficing](https://mlsanity.com/paper/2308.08291/) (2023)

## Built on by (most cited first, 1 of 1)

- [Maximally Robust Satisficing Bayesian Optimization](https://mlsanity.com/paper/2607.13652/) (2026)

## Abstract (arXiv)

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.