When I am running cross validation on the training set for a binary classification problem, what metric should I use if I am only interested in obtaining the largest AUC (area under receiver operating characteristic Curve) value of the corresponding test set, AUC as the metric in the training set (available in caret package in r) or other cross-validation error metric such as Bernoulli deviance and 0-1 loss?
Ref for Bernoulli deviance: Logistic Regression: Bernoulli vs. Binomial Response Variables