An Online Learning Approach to Improving the Quality of Crowd-Sourcing

We consider a crowd-sourcing problem where in the process of labeling massive data sets, multiple labelers with unknown annotation quality must be selected to perform the labeling task for each incoming data sample or task, with the results aggregated using for example simple or weighted majority voting rule. In this paper, we approach this labeler selection problem in an online learning framework, whereby the quality of the labeling outcome by a specific set of labelers is estimated so that the learning algorithm over time learns to use the most effective combinations of labelers. This type of online learning in some sense falls under the family of multi-armed bandit (MAB) problems, but with a distinct feature not commonly seen: since the data is unlabeled to begin with and the labelers' quality is unknown, their labeling outcome (or reward in the MAB context) cannot be readily verified; it can only be estimated against the crowd and be known probabilistically. We design an efficient online algorithm LS_OL using a simple majority voting rule that can differentiate high and low quality labelers over time, and is shown to have a regret (with respect to always using the optimal set of labelers) of O(log
²
T ) uniformly in time under mild assumptions on the collective quality of the crowd, thus regret free in the average sense. We discuss further performance improvement by using a more sophisticated majority voting rule, and show how to detect and filter out “bad” (dishonest, malicious or very incompetent) labelers to further enhance the quality of crowd-sourcing. Extension to the case when a labeler's quality is task-type dependent is also discussed using techniques from the literature on continuous arms. We establish a lower bound on the order of O(log T D
₂
(T )), where D
₂
(T) is an arbitrary function such that D
₂
(T ) > O(1). We further provide a matching upper bound through a minor modification of the algorithm we proposed and studied earlier on. We present numerical results using both simulation and set of images labeled by amazon mechanic turks.