I'm reading a paper that states that trajectories $\tau$ are sampled from a distribution $\pi$ and they use the notation for the expectation $\mathbb{E}_{\tau \sim \pi}$ but also use $\mathbb{E}_{\tau | \pi}$ and I can't say I'm sure what the difference really is.
While $\mathbb{E}_{\tau \sim \pi}$ is obvious in that the trajectories, $\tau$, are sampled from the distribution $\pi$, the latter isn't as obvious to me.
Thank you.
The paper in question is this one: https://arxiv.org/pdf/1502.05477.pdf#appendix.A