This is a question I have after reading this (page 41) https://tel.archives-ouvertes.fr/tel-01816069/document
I wonder how is it possible to condition the expectation on the right-hand side without having the left-hand side also conditioned on $\mathcal F_t$ and $\tilde \theta \in \Theta^{opt}_t$. Is there any property on conditional expectations that I'm probably missing? It's like having two random variables $X$ and $Y$ such that $X\leq Y$ and then writing $X \leq \mathbb E[Y|\mathcal G]$ for some sigma algebra $\mathcal G$. Am I wrong?
