In active learning, where a learning algorithm has to purchase the labels of its training examples, it is often assumed that there is only one labeler available to label examples, and that this labeler is noise-free. In reality, it is possible that there are multiple labelers available (such as human labelers in the online annotation tool Amazon Mechanical Turk) and that each such labeler has a different cost and accuracy. We address the active learning problem with multiple labelers where each labeler has a different (known) cost and a different (unknown) accuracy. Our approach uses the idea of adjusted cost, which allows labelers with different costs and accuracies to be directly compared. This allows our algorithm to find low-cost combinations of labelers that result in high-accuracy labelings of instances. Our algorithm further reduces costs by pruning under-performing labelers from the set under consideration, and by halting the process of estimating the accuracy of the labelers as early as it can. We found that our algorithm often outperforms, and is always competitive with, other algorithms in the literature.

We explore the problem of budgeted machine learning, in which the learning algorithm has free access to the training examples' labels but has to pay for each attribute that is specified. This learning model is appropriate in many areas, including medical applications. We present new algorithms for choosing which attributes to purchase of which examples in the budgeted learning model based on algorithms for the multi-armed bandit problem. All of our approaches outperformed the current state of the art. Furthermore, we present a new means for selecting an example to purchase after the attribute is selected, instead of selecting an example uniformly at random, which is typically done. Our new example selection method improved performance of all the algorithms we tested, both ours and those in the literature.