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Bayesian Optimization for Min Max Optimization

Paper presented at Workshop on Real World Experiment Design and Active Learning at ICML 2020, Virtual Workshop, 18 July 2020
: Weichert, Dorina; Kister, A.

Fulltext urn:nbn:de:0011-n-5967915 (317 KByte PDF)
MD5 Fingerprint: 0098a5afdf4441239847fe961baae85d
Created on: 21.7.2020

2020, 11 pp.
Workshop on Real World Experiment Design and Active Learning <2020, Online>
International Conference on Machine Learning (ICML) <37, 2020, Online>
Presentation, Electronic Publication
Fraunhofer IAIS ()
Bayesian Optimization; Min Max Optimization; Worst Case Robustness

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.