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I am reading the following statement from a paper on the algorithms of inverse reinforcement learning:

'Using the RL Algorithm, compute the optimal policy $\pi$ for the MDP using the rewards $R = w^T\phi$.'

I am not sure what this statement means. What is the expected output of this statement? If I want to compute the optimal policy, especially in a situation when I have infinite state space, how will this possibly turn out?

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  • $\begingroup$ Please improve the question by specifying what $w^T\phi$ is and (at best) add the reference where you have read this. $\endgroup$
    – steffen
    Dec 21, 2015 at 11:50

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A policy is a function from the state space to the action space; how to encode it is up to you. There many ways of approximating infinite spaces, but, seeing that the formula for reward is expressed in vector notation, the spaces are probably finite, and the optimal policy can be implemented as a table lookup.

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    $\begingroup$ Thanks for your reply. The reward function here is in terms of $\phi$, the features and $w$, the corresponding weights. Having said this, is it still possible that the state space is infinite? $\endgroup$
    – cgo
    Dec 15, 2015 at 18:21
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    $\begingroup$ The feature space is a finite approximation of the state space, which could be infinite. $\endgroup$
    – Don Reba
    Dec 15, 2015 at 22:52

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