Given a classifier and a dataset, let's say we want a) to find a classifier that separates classes such that F1 score is the best b) to find a classifier that separates classes such that AUC is best. Is the decision boundary in both cases same? Does finding the best AUC means that we already found best F1 score and Accuracy, or it isn't valid assumption?
I am training two classifiers, one that optimizes AUC and the other that optimizes F1 score. In both of these F1 score and AUC is the same.