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Is there any actual difference between these 2 definitions of a state value function?
The definition of the value function in TRPO paper is
\begin{align}
V_\pi(s_t) &= \mathbb{E}_{a_t,s_{t+1},\ldots} \left[ \sum_{l=0}^{\infty} \gamma^l r(s_{t+l}) \right], \\[10pt]
a_t &\sim \pi(...
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