Disagreement-based Active Learning in Online Settings

We study online active learning for classifying streaming instances within the framework of statistical learning theory. At each time, the learner decides whether to query the label of the current instance. If the decision is to not query, the learner predicts the label and receives no feedback on the correctness of the prediction. The objective is to minimize the number of queries while constraining the number of prediction errors over a horizon of length $T$. We consider a general concept space with a finite VC dimension $d$ and adopt the agnostic setting. We develop a disagreement-based online learning algorithm and establish its $O(dT^{\frac{2-2\alpha}{2-\alpha}}\log^2 T)$ label complexity and bounded regret in terms of classification errors, where $\alpha$ is the Tsybakov noise parameter. The proposed algorithm is shown to outperform existing online active learning algorithms as well as extensions of representative offline algorithms developed under the PAC setting.