# Adversarially Robust Optimization with Gaussian Processes

arXiv: https://arxiv.org/abs/1810.10775 · HTML: https://mlsanity.com/paper/1810.10775/

## Key facts

- Cited by 62 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Oct 2018.

## Built on by (most cited first, 30 of 62)

- [Misspecified Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2111.05008/) (2021)
- [Robust Multi-Objective Bayesian Optimization Under Input Noise](https://mlsanity.com/paper/2202.07549/) (2022)
- [Thinking inside the box: A tutorial on grey-box Bayesian optimization](https://mlsanity.com/paper/2201.00272/) (2022)
- [Value-at-Risk Optimization with Gaussian Processes](https://mlsanity.com/paper/2105.06126/) (2021)
- [Multi-Fidelity Bayesian Optimization with Unreliable Information Sources](https://mlsanity.com/paper/2210.13937/) (2022)
- [Risk-averse Heteroscedastic Bayesian Optimization](https://mlsanity.com/paper/2111.03637/) (2021)
- [Distributionally Robust Model-based Reinforcement Learning with Large State Spaces](https://mlsanity.com/paper/2309.02236/) (2023)
- [Distributionally Robust Bayesian Optimization with varphi-divergences](https://mlsanity.com/paper/2203.02128/) (2022)
- [Randomized Gaussian Process Upper Confidence Bound with Tighter Bayesian Regret Bounds](https://mlsanity.com/paper/2302.01511/) (2023)
- [Regret Bounds for Expected Improvement Algorithms in Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2203.07875/) (2022)
- [Bias-Robust Bayesian Optimization via Dueling Bandits](https://mlsanity.com/paper/2105.11802/) (2021)
- [A Robust Phased Elimination Algorithm for Corruption-Tolerant Gaussian Process Bandits](https://mlsanity.com/paper/2202.01850/) (2022)
- [Active learning for distributionally robust level-set estimation](https://mlsanity.com/paper/2102.04000/) (2021)
- [Gaussian Process Upper Confidence Bound Achieves Nearly-Optimal Regret in Noise-Free Gaussian Process Bandits](https://mlsanity.com/paper/2502.19006/) (2025)
- [Robust Bandit Learning with Imperfect Context](https://mlsanity.com/paper/2102.05018/) (2021)
- [Batch Bayesian Optimization for Replicable Experimental Design](https://mlsanity.com/paper/2311.01195/) (2023)
- [Direct-Search for a Class of Stochastic Min-Max Problems](https://mlsanity.com/paper/2102.11386/) (2021)
- [Max-Min Grouped Bandits](https://mlsanity.com/paper/2111.08862/) (2021)
- [Golem: An algorithm for robust experiment and process optimization](https://mlsanity.com/paper/2103.03716/) (2021)
- [Measuring the robustness of Gaussian processes to kernel choice](https://mlsanity.com/paper/2106.06510/) (2021)
- [Bayesian Active Learning in the Presence of Nuisance Parameters](https://mlsanity.com/paper/2310.14968/) (2023)
- [Efficient Robust Bayesian Optimization for Arbitrary Uncertain Inputs](https://mlsanity.com/paper/2310.20145/) (2023)
- [Adversarial Robustness Guarantees for Gaussian Processes](https://mlsanity.com/paper/2104.03180/) (2021)
- [Adversarial Attacks on Gaussian Process Bandits](https://mlsanity.com/paper/2110.08449/) (2021)
- [Bayesian Optimization for Distributionally Robust Chance-constrained Problem](https://mlsanity.com/paper/2201.13112/) (2022)
- [Robust expected improvement for Bayesian optimization](https://mlsanity.com/paper/2302.08612/) (2023)
- [Lower Bounds for Time-Varying Kernelized Bandits](https://mlsanity.com/paper/2410.16692/) (2024)
- [Adversarial Causal Bayesian Optimization](https://mlsanity.com/paper/2307.16625/) (2023)
- [Robust Entropy Search for Safe Efficient Bayesian Optimization](https://mlsanity.com/paper/2405.19059/) (2024)
- [Improving SAM Requires Rethinking its Optimization Formulation](https://mlsanity.com/paper/2407.12993/) (2024)

## Abstract (arXiv)

In this paper, we consider the problem of Gaussian process (GP) optimization with an added robustness requirement: The returned point may be perturbed by an adversary, and we require the function value to remain as high as possible even after this perturbation. This problem is motivated by settings in which the underlying functions during optimization and implementation stages are different, or when one is interested in finding an entire region of good inputs rather than only a single point. We show that standard GP optimization algorithms do not exhibit the desired robustness properties, and provide a novel confidence-bound based algorithm StableOpt for this purpose. We rigorously establish the required number of samples for StableOpt to find a near-optimal point, and we complement this guarantee with an algorithm-independent lower bound. We experimentally demonstrate several potential applications of interest using real-world data sets, and we show that StableOpt consistently succeeds in finding a stable maximizer where several baseline methods fail.