You are using one approach for the classification where to teach the agent not by...

Unsupervised learning seems much harder: the goal is to have the computer learn how to do something that we don't tell it how to do! The approach is to teach the agent not by giving explicit categorizations, but by using some sort of reward system to indicate success. Note that this type of training will generally fit into the decision problem framework because the goal is not to produce a classification but to make decisions that maximize rewards. This approach nicely generalizes to the real world, where agents might be rewarded for doing certain actions and punished fordoing others.