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1

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 ...


2

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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