Bayesian Optimization for Min Max Optimization

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.