Auditing: Active Learning with Outcome-Dependent Query Costs

We propose a learning setting in which unlabeled data is free, and the cost of a label depends on its value, which is not known in advance. We study binary classification in an extreme case, where the algorithm only pays for negative labels. Our motivation are applications such as fraud detection, in which investigating an honest transaction should be avoided if possible. We term the setting auditing, and consider the auditing complexity of an algorithm: The number of negative points it labels to learn a hypothesis with low relative error. We design auditing algorithms for thresholds on the line and axis-aligned rectangles, and show that with these algorithms, the auditing complexity can be significantly lower than the active label complexity.