2
we start with
$\frac{\partial}{\partial \theta} \mathbb E_{q(\mathbf w\mid\theta)}[f(\mathbf w, \theta)]$
using definition of expectation for continuous case:
$\mathbb E[X] = \int xp(x) dx$
for the first equation we get:
$\frac{\partial}{\partial \theta} \int f(\mathbf w, \theta)q(\mathbf w \mid \theta) d\mathbf w$
we swap $q(\mathbf w \mid \...
1
You cannot do this:
$\mathop{\mathbb{E}_\pi }[r(\tau )\bigtriangledown log \pi (\tau )] \\= \mathop{\mathbb{E}_\pi }[r(\tau )] \,\, \mathop{\mathbb{E}_\pi }[\bigtriangledown log \pi (\tau )]$
That is because $r(\tau )$ and $\bigtriangledown log \pi (\tau )$ are correlated by their dependence on $\tau$. In a simpler concrete example, if your expectation ...
1
When we say that we have $N$ points that were "drawn from the probability distribution or probability density", this means that every point $x_n$ had the correct probability $p(x_n)$ of being sampled from the distribution when we were sampling our $n^{th}$ point.
For example, suppose that we wish to compute/estimate the expected value of a distribution ...
Only top voted, non community-wiki answers of a minimum length are eligible
