1
$\begingroup$

In his original GAN paper Goodfellow gives a game theoretic perspective for GANs:

\begin{equation} \underset{G}{\min}\, \underset{D}{\max}\, V\left(D,G \right) = \mathbb{E}_{x\sim\mathit{p}_{\textrm{data}}\left(x \right)} \left[\textrm{log}\, D \left(x \right) \right] + \mathbb{E}_{z\sim\mathit{p}_{\textrm{z}}\left(z \right)} \left[\textrm{log} \left(1 - D \left(G \left(z \right)\right)\right) \right] \end{equation}

I think I understand this formula, at least it makes sense to me. What I don't understand is that he writes in his NIPS tutorial:

In the minimax game, the discriminator minimizes a cross-entropy, but the generator maximizes the same cross-entropy.

Why does he write that the discriminator minimizes the cross-entropy while the generator maximizes it? Shouldn't it be the other way around? At least that is how I understand $\underset{G}{\min}\, \underset{D}{\max}\, V\left(D,G \right)$.

I guess this shows that I have a fundamental error in my understanding. Could anyone clarify what I'm missing here?

$\endgroup$
1
$\begingroup$

Your mistake is that you think that the referenced $V(D,G)$ is the deifinition of the cross entropy! Indeed, the cross entropy is defined base on the negative value of the $V(D,G)$. Hence, if you consider the minus behind the $V(D,G)$ ($-V(D,G)$) the sentence will be meaningful.

| improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.