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Wow, that's a really confusing example, if I were you I would check out some other RL resources. I wouldn't consider h being the last step and h-1 being the previous step. In terms of steps of iterations of the dynamic programming algorithm, h is actually the first step, h-1 the next step and so on. Viewing it in these terms it makes sense that the Value of ...


That's exactly the point of the Policy Gradient Theorem. Let's go through he proof of this theorem - it relies on our ability to "loop" the reward expression $J(\theta,s)$, expressing it through $J(\theta,s')$ in the next state: $$J(\theta,s) = \mathbb{E}_{\tau\sim\pi_\theta}\left[ R(\tau) | s_0 = s\right]$$ $$\begin{align} J(\theta,s) & = \...

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