GAN: The Optimal Discriminator

The problem, from first principles

The GAN paper shows that for a fixed generator, the best discriminator outputs the ratio of the data density to the sum of the two densities. When the generator matches the data, this ratio is one half everywhere, the equilibrium of the game.

From theory to code

Implement optimal_discriminator(p_data, p_model), returning the density ratio element-wise.

Constraints

• Densities are nonnegative and not both zero at any point.

Hints