# Disagreement-based Active Learning in Online Settings

## TL;DR

This paper introduces a disagreement-based online active learning algorithm for streaming data that minimizes label queries while controlling prediction errors, achieving near-optimal label complexity under Tsybakov noise.

## Contribution

It develops a novel online active learning algorithm with theoretical guarantees and demonstrates its near-optimal label complexity under general hypothesis spaces and noise conditions.

## Key findings

- Algorithm achieves label complexity of O(dT^{(2-2α)/(2-α)} log^2 T)
- Proves a matching lower bound up to poly-logarithmic factors
- Addresses tradeoff between label complexity and regret

## Abstract

We study online active learning for classifying streaming instances within the framework of statistical learning theory. At each time, the learner either queries the label of the current instance or predicts the label based on past seen examples. The objective is to minimize the number of queries while constraining the number of prediction errors over a horizon of length $T$. We develop a disagreement-based online learning algorithm for a general hypothesis space and under the Tsybakov noise. We show that the proposed algorithm has a label complexity of $O(dT^{\frac{2-2\alpha}{2-\alpha}}\log^2 T)$ under a constraint of bounded regret in terms of classification errors, where $d$ is the VC dimension of the hypothesis space and $\alpha$ is the Tsybakov noise parameter. We further establish a matching (up to a poly-logarithmic factor) lower bound, demonstrating the order optimality of the proposed algorithm. We address the tradeoff between label complexity and regret and show that the algorithm can be modified to operate at a different point on the tradeoff curve.