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A set of dynamic strategies by which an algorithm can learn the structure of an environment online by adaptively taking actions associated with different rewards so as to maximize the rewards earned.

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Two different value functions formulations, how can I reconcile them?

They are the same, but the first formula is more general and allows stochastic rewards. Remarks $$p(s', r \mid s, a)$$ implies that the reward $r$ is dependent on both a state $s$ and an action $a …
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