We consider the problems of online and one-pass maximization of the area under the ROC curve (AUC). AUC maximization is hard even in the offline setting and thus solutions often make some compromises. Existing results for the online problem typically optimize for some proxy defined via surrogate losses instead of maximizing the real AUC. This approach is confirmed by results showing that the optimum of these proxies, over the set of all (measurable) functions, maximize the AUC. The problem is that—in order to meet the strong requirements for per round run time complexity—online methods typically work with restricted hypothesis classes and this, as we show, corrupts the above compatibility and causes the methods to converge to suboptimal solutions even in some simple stochastic cases. To remedy this, we propose a different approach and show that it leads to asymptotic optimality. Our theoretical claims and considerations are tested by experiments on real datasets, which provide empirical justification to them.
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