Why there is theta in index of gradient symbol in gradient descent update formula for MAML?

Question

In this MAML paper, they use following formula of gradient descent update (see page 3, algorithm 1):

$$ \varTheta '\ =\varTheta \ −\ \alpha \nabla _{\varTheta }\mathcal{L}_{\mathcal{T}_{i}}( f_{\varTheta }) $$

My question is, what is the reason of having theta in subscript after gradient (nabla) ?

Specifically, why is it not like this:

$$ \displaystyle \varTheta '\ =\varTheta \ −\ \alpha \nabla \mathcal{L}_{\mathcal{T}_{i}}( f_{\varTheta }) \ $$

In other words why is not enough to tell it like just gradient of loss function?

Answer 1

That means gradient with respect to $\theta$. In the context, there is little uncertainty and probably anyone reading the paper can understand that it is gradient wrt $\theta$ even if they hadn't used the subscript notation but there is no harm in being precise, especially in published work.

It's like writing $\frac{\partial f}{\partial \theta}$, instead of $f'$.