# Bayesian Optimization for Min Max Optimization

arXiv: https://arxiv.org/abs/2107.13772 · HTML: https://mlsanity.com/paper/2107.13772/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 21 references that are in the map.
- First posted on arXiv 29 Jul 2021.

## Builds on (most cited first, 9 of 9)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Max-value Entropy Search for Multi-Objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/2009.01721/) (2020)
- [Adversarially Robust Optimization with Gaussian Processes](https://mlsanity.com/paper/1810.10775/) (2018)
- [BoTorch: A Framework for Efficient Monte-Carlo Bayesian Optimization](https://mlsanity.com/paper/1910.06403/) (2019)
- [Bayesian Optimization with Expensive Integrands](https://mlsanity.com/paper/1803.08661/) (2018)
- [Noisy-Input Entropy Search for Efficient Robust Bayesian Optimization](https://mlsanity.com/paper/2002.02820/) (2020)
- [Integrals over Gaussians under Linear Domain Constraints](https://mlsanity.com/paper/1910.09328/) (2019)
- [Mixed Strategies for Robust Optimization of Unknown Objectives](https://mlsanity.com/paper/2002.12613/) (2020)

## Built on by (most cited first, 2 of 2)

- [Robust Entropy Search for Safe Efficient Bayesian Optimization](https://mlsanity.com/paper/2405.19059/) (2024)
- [Bayesian Optimization for Function-Valued Responses under Min-Max Criteria](https://mlsanity.com/paper/2512.07868/) (2025)

## Abstract (arXiv)

A solution that is only reliable under favourable conditions is hardly a safe solution. Min Max Optimization is an approach that returns optima that are robust against worst case conditions. We propose algorithms that perform Min Max Optimization in a setting where the function that should be optimized is not known a priori and hence has to be learned by experiments. Therefore we extend the Bayesian Optimization setting, which is tailored to maximization problems, to Min Max Optimization problems. While related work extends the two acquisition functions Expected Improvement and Gaussian Process Upper Confidence Bound; we extend the two acquisition functions Entropy Search and Knowledge Gradient. These acquisition functions are able to gain knowledge about the optimum instead of just looking for points that are supposed to be optimal. In our evaluation we show that these acquisition functions allow for better solutions - converging faster to the optimum than the benchmark settings.