Surrogate losses in passive and active learning

Abstract

Active learning is a type of sequential design for supervised machine learning, in which the learning algorithm sequentially requests the labels of selected instances from a large pool of unlabeled data points. The objective is to produce a classifier of relatively low risk, as measured under the $0$-$1$ loss, ideally using fewer label requests than the number of random labeled data points sufficient to achieve the same. This work investigates the potential uses of surrogate loss functions in the context of active learning. Specifically, it presents an active learning algorithm based on an arbitrary classification-calibrated surrogate loss function, along with an analysis of the number of label requests sufficient for the classifier returned by the algorithm to achieve a given risk under the $0$-$1$ loss. Interestingly, these results cannot be obtained by simply optimizing the surrogate risk via active learning to an extent sufficient to provide a guarantee on the $0$-$1$ loss, as is common practice in the analysis of surrogate losses for passive learning. Some of the results have additional implications for the use of surrogate losses in passive learning.