The point is that supervised training on large networks requires millions or billions of examples. In RL, that means potentially billions of execution trajectories, which can be really expensive if you're executing on an actual, physical robot. And even then, supervised classification objectives are more informative than just a scalar reward: when a supervised system makes a wrong prediction you don't just tell it "sorry, that's wrong", you also tell it what the right prediction would have been. That extra information is really valuable for learning.

In the black-box RL setting, you only see whether what you did was right or wrong, not what the right thing would have been to do. And unlikely a classification system where the output space is relatively small (ImageNet has 1000 classes), an RL agent is searching over an exponentially large space of possible trajectories. Which means that without some additional source of supervision you can spend a long time wandering in the wilderness with no idea of whether what you're doing is reasonable or how to get any reward at all. And when you do get some reward, you have no idea which of the possibly hundreds or thousands of actions you took deserves the credit.

A lot of recent RL research is about finding additional sources of supervision, such as training an agent to mimic the policy of an "expert" (e.g., a search algorithm that runs in a simulator to find an optimal solution, but which requires too much computation to actually apply directly at test time, as in http://arxiv.org/abs/1504.00702), or coming up with proxy objectives like "empowerment" or "curiosity" (which you can define in terms of information theoretic quantities, such as mutual information between the agents' action sequence and future state, e.g. http://arxiv.org/abs/1509.08731) to supplement the actual reward signal. This latter path, the notion of "intrinsic reward" that paulsutter alluded to, is in some sense the merger of RL with unsupervised learning, and a lot of the power is that you're getting new reward signals constantly, not just when you finally manage to achieve some arbitrarily difficult task.