One-Pass AUC Optimization

AUC is an important performance measure and many algorithms have been devoted to AUC optimization, mostly by minimizing a surrogate convex loss on a training data set. In this work, we focus on one-pass AUC optimization that requires going through the training data only once without storing the entire training dataset, where conventional online learning algorithms cannot be applied directly because AUC is measured by a sum of losses defined over pairs of instances from different classes. We develop a regression-based algorithm which only needs to maintain the first and second-order statistics of training data in memory, resulting a storage requirement independent from the size of training data. To efficiently handle high-dimensional data, we develop a randomized algorithm that approximates the covariance matrices by low-rank matrices. We verify, both theoretically and empirically, the effectiveness of the proposed algorithm.