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Most introductions to the field of MDPs and Reinforcement learning focus exclusively on domains where space and action variables are integers (and finite). This way we are introduced quickly to Value Iteration, Q-Learning, and the like.

However the most interesting applications (say, flying helicopters) of RL and MDPs involve continuous state space and action spaces. I'd like to go beyond basic introductions and focus on these cases but I am not sure how to get there.

What areas do I need to know or study to understand these cases in depth?

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There is a small survey of continuous states, actions and time in reinforcement learning in my thesis proposal.

Regarding books, Reinforcement Learning: State-of-the-Art seems to be pretty up-to-date from the excerpts I've read.

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