GAN Minmax Game


## Training GAN
Aims to $D(G(z))$ to be close to 1, i.e. discriminator is fooled
### Gradient descent on generator
![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F19a41272-13ca-4ad9-b94a-c3fe8dbd031f%2FUntitled.png?table=block&id=17e51d57-7290-4e22-8703-8a64cf6e1b95&cache=v2)
If $G$ is very bad compared to $D$, then we have almost zero gradient. Hence, $-D$ term can be used
![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F5c0d0cce-916a-44e9-a971-c7201830e7db%2FUntitled.png?table=block&id=5841e261-a075-413d-860c-0186cb106361&cache=v2)

### Gradient ascent on discriminator
Generator $\theta$ and Discriminator $\phi$ has very different objective so hard to train stable







