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Adversarially Robust Optimization with Gaussian Processes

arXiv 1810.10775 ↗First posted 25 Oct 2018stat.ML cs.LGcited by 62

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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.

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

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Citing papers per year: 2021: 15; 2022: 10; 2023: 12; 2024: 9; 2025: 7; 2026: 9.

62 papers.

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  1. 2021Misspecified Gaussian Process Bandit Optimizationcited by 55
  2. 2022Robust Multi-Objective Bayesian Optimization Under Input Noisecited by 37
  3. 2022Thinking inside the box: A tutorial on grey-box Bayesian optimizationcited by 26
  4. 2021Value-at-Risk Optimization with Gaussian Processescited by 20
  5. 2022Multi-Fidelity Bayesian Optimization with Unreliable Information Sourcescited by 18
  6. 2021Risk-averse Heteroscedastic Bayesian Optimizationcited by 17
  7. 2023Distributionally Robust Model-based Reinforcement Learning with Large State Spacescited by 17
  8. 2022Distributionally Robust Bayesian Optimization with varphi-divergencescited by 16
  9. 2023Randomized Gaussian Process Upper Confidence Bound with Tighter Bayesian Regret Boundscited by 16
  10. 2022Regret Bounds for Expected Improvement Algorithms in Gaussian Process Bandit Optimizationcited by 15
  11. 2021Bias-Robust Bayesian Optimization via Dueling Banditscited by 11
  12. 2022A Robust Phased Elimination Algorithm for Corruption-Tolerant Gaussian Process Banditscited by 11
38 more
  1. 2021Active learning for distributionally robust level-set estimationcited by 10
  2. 2025Gaussian Process Upper Confidence Bound Achieves Nearly-Optimal Regret in Noise-Free Gaussian Process Banditscited by 9
  3. 2021Robust Bandit Learning with Imperfect Contextcited by 8
  4. 2023Batch Bayesian Optimization for Replicable Experimental Designcited by 8
  5. 2021Direct-Search for a Class of Stochastic Min-Max Problemscited by 7
  6. 2021Max-Min Grouped Banditscited by 7
  7. 2021Golem: An algorithm for robust experiment and process optimizationcited by 6
  8. 2021Measuring the robustness of Gaussian processes to kernel choicecited by 6
  9. 2023Bayesian Active Learning in the Presence of Nuisance Parameterscited by 6
  10. 2023Efficient Robust Bayesian Optimization for Arbitrary Uncertain Inputscited by 6
  11. 2021Adversarial Robustness Guarantees for Gaussian Processescited by 5
  12. 2021Adversarial Attacks on Gaussian Process Banditscited by 5
  13. 2022Bayesian Optimization for Distributionally Robust Chance-constrained Problemcited by 5
  14. 2023Robust expected improvement for Bayesian optimizationcited by 5
  15. 2024Lower Bounds for Time-Varying Kernelized Banditscited by 5
  16. 2023Adversarial Causal Bayesian Optimizationcited by 4
  17. 2024Robust Entropy Search for Safe Efficient Bayesian Optimizationcited by 4
  18. 2024Improving SAM Requires Rethinking its Optimization Formulationcited by 4
  19. 2024Regret Analysis for Randomized Gaussian Process Upper Confidence Boundcited by 4
  20. 2024Sample-efficient Bayesian Optimisation Using Known Invariancescited by 4
  21. 2026Tighter Regret Lower Bound for Gaussian Process Bandits with Squared Exponential Kernel in Hyperspherecited by 4
  22. 2022Distributed saddle point problems for strongly concave-convex functionscited by 3
  23. 2022Learning Representation for Bayesian Optimization with Collision-free Regularizationcited by 3
  24. 2023Robust Bayesian Target Value Optimizationcited by 3
  25. 2023Robust Bayesian Satisficingcited by 3
  26. 2023Stochastic Bayesian Optimization with Unknown Continuous Context Distribution via Kernel Density Estimationcited by 3
  27. 2024Expected Diverse Utility (EDU): Diverse Bayesian Optimization of Expensive Computer Simulatorscited by 3
  28. 2025BILBO: BILevel Bayesian Optimizationcited by 3
  29. 2025Wasserstein Distributionally Robust Bayesian Optimization with Continuous Contextcited by 3
  30. 2026Batched Kernelized Bandits: Refinements and Extensionscited by 3
  31. 2021Cost-Efficient Online Hyperparameter Optimizationcited by 2
  32. 2021Bayesian Optimization for Min Max Optimizationcited by 2
  33. 2024Targeted Variance Reduction: Robust Bayesian Optimization of Black-Box Simulators with Noise Parameterscited by 2
  34. 2024Sharpness-Aware Black-Box Optimizationcited by 2
  35. 2024Practical Bayesian Algorithm Execution via Posterior Samplingcited by 2
  36. 2022A Simple Structure For Building A Robust Modelcited by 1
  37. 2025A Framework for Finding Local Saddle Points in Two-Player Zero-Sum Black-Box Gamescited by 1
  38. 2025Robust Satisficing Gaussian Process Bandits Under Adversarial Attackscited by 1

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