I am training a binary classifier in a dataset using AUC as a score. The dataset has two main groups (we will refer to them as good and bad population). A property that this dataset has is having a higher proportion of target = 1 in the bad population.
For this reason, a relatively dummy classifier would give higher scores to the bad population and lower scores to the good population. In fact, the AUC of the classifier could be pretty high globally, and, when looking at the AUC inside both populations separately, the AUC might be really low in both of them.
I want to avoid this behavior. In fact, I am willing to sacrifice some AUC in the global population such that the AUC in each group is not very low. An idea that I had was using the harmonic mean of the AUC of both groups as a metric instead of the general AUC. However, this might not really help a classifier in a natural way.
Are there any papers/techniques/software that can help me in solving this problem in a more natural way?