EGAN Paper With Confusing Notation

Question

I am reading a research paper that tries to fix some issues with GAN, but for one of the equations, the paper does not fully explain where it comes from and why it works. Although the overall algorithm for EGAN is straight forward, I wish to understand it a little better.

The paper uses an evolutionary approach to fix stuff like instability and mode collapsing. A fitness function for evaluating the different generators is give as:

Where f_d is:

and f_q is:

What I'm focusing on is f_d = -log||delta_d - E_x[log(D(x))] - E_z[log(D(G(z)))]||.

In f_d, what does delta_d represent. It was not defined in the paper so I figured maybe it was very typical notation for something so I looked around but could not find anything. The only things I know is from what it says in the paper, and the paper that the writers referenced to create the equation (proofs >.<)

What I know right now is the entirety of f_d represents what the paper calls the diversity fitness score. I also know that the second part of the equation is the same as the loss function for a discriminator so it could be re written as f_d = -log(delta_d + loss_d). But what is delta_d? and how does this equation properly evaluate the diversity of the generated samples?

Answer 1

$\nabla_D$ means the gradient w.r.t. the discriminator parameters. The authors explained below as "the log gradient value of updating D".

BTW it's not standard to write something like $\nabla-a-b$ as this paper, which confuses readers as "$\nabla$ minus $a$ minus $b$". It's much better to write $-\nabla(a+b)$.