  Online Active Learning (OAL) aims to manage unlabeled datastream by
selectively querying the label of data. OAL is applicable to many real-world
problems, such as anomaly detection in health-care and finance. In these
problems, there are two key challenges: the query budget is often limited; the
ratio between classes is highly imbalanced. In practice, it is quite difficult
to handle imbalanced unlabeled datastream when only a limited budget of labels
can be queried for training. To solve this, previous OAL studies adopt either
asymmetric losses or queries (an isolated asymmetric strategy) to tackle the
imbalance, and use first-order methods to optimize the cost-sensitive measure.
However, the isolated strategy limits their performance in class imbalance,
while first-order methods restrict their optimization performance. In this
paper, we propose a novel Online Adaptive Asymmetric Active learning algorithm,
based on a new asymmetric strategy (merging both asymmetric losses and queries
strategies), and second-order optimization. We theoretically analyze its
mistake bound and cost-sensitive metric bounds. Moreover, to better balance
performance and efficiency, we enhance our algorithm via a sketching technique,
which significantly accelerates the computational speed with quite slight
performance degradation. Promising results demonstrate the effectiveness and
efficiency of the proposed methods.
