  Adequate evaluation of an information retrieval system to estimate future
performance is a crucial task. Area under the ROC curve (AUC) is widely used to
evaluate the generalization of a retrieval system. However, the objective
function optimized in many retrieval systems is the error rate and not the AUC
value. This paper provides an efficient and effective non-linear approach to
optimize AUC using additive regression trees, with a special emphasis on the
use of multi-class AUC (MAUC) because multiple relevance levels are widely used
in many ranking applications. Compared to a conventional linear approach, the
performance of the non-linear approach is comparable on binary-relevance
benchmark datasets and is better on multi-relevance benchmark datasets.
