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 decision maker decides whether to query for the label of the current instance and, in the event of no query, self labels the instance. The objective is to minimize the number of queries while constraining the number of classification 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 propose a disagreement-based online learning algorithm and establish its $O(d\log^2 T)$ label complexity and $\Theta(1)$ (i.e., bounded) classification errors in excess to the best classifier in the concept space under the Massart bounded noise condition.