Supervised learning deals with the inference of a distribution over an output or label space $\CY$ conditioned on points in an observation space $\CX$, given a training dataset $D$ of pairs in $\CX \times \CY$. However, in a lot of applications of interest, acquisition of large amounts of observations is easy, while the process of generating labels is time-consuming or costly. One way to deal with this problem is {\em active} learning, where points to be labelled are selected with the aim of creating a model with better performance than that of an model trained on an equal number of randomly sampled points. In this paper, we instead propose to deal with the labelling cost directly: The learning goal is defined as the minimisation of a cost which is a function of the expected model performance and the total cost of the labels used. This allows the development of general strategies and specific algorithms for (a) optimal stopping, where the expected cost dictates whether label acquisitio...