Active Learning 

Active learning is a subfield of artificial intelligence where an AI agent iteratively chooses new information it would like to learn. This machine learning methodology allows a system to learn much more quickly and with fewer data points since it can choose what it wants to learn next and train itself on the new information rather than learning new things at random. The name comes from active learning in educational settings where students are taught a concept and then immediately asked to solve a problem using the concept they just learned. This methodology has great results both in the physical classroom and in applied machine learning. 

The following diagram shows the active learning methodology. Where a model learns from the information that is known already in the "Labeled Training Data" and then selects another piece of information it wants to know by querying the "Data Labeling Service." The AI agent would be able to learn faster since it selects what it is "curious" about. 

Formalized Definitions:

I copied these definitions from this Wikipedia page.

Let T be the total set of all data under consideration. For example, in a protein engineering problem, T would include all proteins that are known to have a certain interesting activity and all additional proteins that one might want to test for that activity.

During each iteration, i, T is broken up into three subsets

Most of the current research in active learning involves the best method to choose the data points for TC,i.