# Robust expected improvement for Bayesian optimization

arXiv: https://arxiv.org/abs/2302.08612 · HTML: https://mlsanity.com/paper/2302.08612/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 73 references that are in the map.
- First posted on arXiv 16 Feb 2023.

## Builds on (most cited first, 15 of 15)

- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Adversarially Robust Optimization with Gaussian Processes](https://mlsanity.com/paper/1810.10775/) (2018)
- [Batched High-dimensional Bayesian Optimization via Structural Kernel Learning](https://mlsanity.com/paper/1703.01973/) (2017)
- [JuMP: A Modeling Language for Mathematical Optimization](https://mlsanity.com/paper/1508.01982/) (2015)
- [Practical heteroskedastic Gaussian process modeling for large simulation experiments](https://mlsanity.com/paper/1611.05902/) (2016)
- [Replication or exploration? Sequential design for stochastic simulation experiments](https://mlsanity.com/paper/1710.03206/) (2017)
- [A supermartingale approach to Gaussian process based sequential design of experiments](https://mlsanity.com/paper/1608.01118/) (2016)
- [Unscented Bayesian Optimization for Safe Robot Grasping](https://mlsanity.com/paper/1603.02038/) (2016)
- [Bayesian optimisation under uncertain inputs](https://mlsanity.com/paper/1902.07908/) (2019)
- [A support vector regression-based multi-fidelity surrogate model](https://mlsanity.com/paper/1906.09439/) (2019)
- [Triangulation candidates for Bayesian optimization](https://mlsanity.com/paper/2112.07457/) (2021)
- [Heteroscedastic Treed Bayesian Optimisation](https://mlsanity.com/paper/1410.7172/) (2014)
- [Distance-distributed design for Gaussian process surrogates](https://mlsanity.com/paper/1812.02794/) (2018)
- [ROC++: Robust Optimization in C++](https://mlsanity.com/paper/2006.08741/) (2020)

## Built on by (most cited first, 5 of 5)

- [Efficient Robust Bayesian Optimization for Arbitrary Uncertain Inputs](https://mlsanity.com/paper/2310.20145/) (2023)
- [Robust Entropy Search for Safe Efficient Bayesian Optimization](https://mlsanity.com/paper/2405.19059/) (2024)
- [Expected Diverse Utility (EDU): Diverse Bayesian Optimization of Expensive Computer Simulators](https://mlsanity.com/paper/2410.01196/) (2024)
- [Targeted Variance Reduction: Robust Bayesian Optimization of Black-Box Simulators with Noise Parameters](https://mlsanity.com/paper/2403.03816/) (2024)
- [Robust Bayesian Optimisation with Unbounded Corruptions](https://mlsanity.com/paper/2511.15315/) (2025)

## Abstract (arXiv)

Bayesian Optimization (BO) links Gaussian Process (GP) surrogates with sequential design toward optimizing expensive-to-evaluate black-box functions. Example design heuristics, or so-called acquisition functions, like expected improvement (EI), balance exploration and exploitation to furnish global solutions under stringent evaluation budgets. However, they fall short when solving for robust optima, meaning a preference for solutions in a wider domain of attraction. Robust solutions are useful when inputs are imprecisely specified, or where a series of solutions is desired. A common mathematical programming technique in such settings involves an adversarial objective, biasing a local solver away from ``sharp'' troughs. Here we propose a surrogate modeling and active learning technique called robust expected improvement (REI) that ports adversarial methodology into the BO/GP framework. After describing the methods, we illustrate and draw comparisons to several competitors on benchmark synthetic exercises and real problems of varying complexity.