What category of AI would a 2048 bot be considered? I have just delved into the realm of AI and from what I can tell its a very vast field of study. I am a game programmer, so AI in games is particularly interesting to me. My question is, what type of AI would a bot that can beat 2048 fall under?

I learned the basics of machine learning, but I wasn't sure if this is how you could apply machine learning. I want to know what category this falls under so I know what to research and learn to make my own bot. Also, if you don't know what 2048 is, check it out here.
I would initially say that you can classify 2048 as a MDP problem.

For this reason, I would consider looking at Reinforcement Learning (an area of Machine Learning). 

Another option, however, more specific would be to look at the performance of Monte Carlo Tree Search.

There is a great discussion in StackOverflow about 2048 different approaches have been tried:
https://stackoverflow.com/questions/22342854/what-is-the-optimal-algorithm-for-the-game-2048