  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
only going through the training data 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.
