  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.
