I can think of two cases when linear function approximation in reinforcement learning is useful: when the state space is large enough, or when the state space is continuous.
I have been reading many materials about this concept, and there are certain concepts that I would like to see in an example rather than in proofs. Is there a more 'gentle' introduction or example of how linear function approximation is applied in reinforcement learning?
Currently, I am lost as to how to formulate it in a program to solve a particular problem. I am looking at Q learning right now, and trying to extend the framework to accommodate linear function approximation. But it seems difficult.
Best Answer
For a gentle introduction, see the Georgia Tech & Udacity course on reinforcement learning. You'll find the early videos in section 8, "Generalization" cover a simple example of how one might formalize a simple problem.
For an example, start with the classic mountain car problem. The full details are nicely spelled out in the technical details section of the wikipedia article, but here's a brief, informal summary:
The developers of the BURLAP (Brown-UMBC Reinforcement Learning and Planning) library have a tutorial on how to solve this problem using least-squares policy iteration, which includes this helpful description of how LSPI relies on function approximation.
BURLAP is in Java, but the prose of the tutorial can be followed without much reference to the code.