So, I am trying to take the derivative of the following equation, because it is needed in an optimization problem. I want to make sure I am on the right track. The equation is:
$ -3 \mathbb E[(w^Tz)^2]^2 $
So my question is, what is:
$ \frac{\delta (-3 \mathbb E[(w^Tz)^2]^2)}{\delta w} = ? $
Please assume here that $w$ is a 2-dimensional column vector, just like $z$. $z$ is also a zero mean, unit variance (joint) random variable. ($w$ is a deterministic vector).
I would like a break down of the steps for evaluating the derivative here - I half syspect the chain rule is involved, however I am getting thrown off by the presence of the expectation operator.
Thanks!