Generative Adiversal Networks (GAN)¶
game theory where a generator competes against an adversary
generator directly produces samples \(x=g(z;\theta)\)
discriminator attempts to distinguish between samples drawn from training data and samples drawn from the generator, it emits the probability \(d(x;\theta)\) that x is real
we can express this as a zero-sum game
\(v(\theta^{(k)}, \theta^{(d)})\) determines the payoff of the discriminator the generator receives \(-v\) as its own payment
each player tries to maximize its payoff $\( g^* = \arg \min_g \max_d v(g,d) \)$
the default choice for \(v\) is $\( v(\theta^{(k)}, \theta^{(d)} = E_{x \sim p_{\text{data}}} \log d(x) + E_{x \sim p_{model}} \log(1 - d(x)) \)$
at convergence the discriminator is unable to distinguish real from the fake thus emits probability 1/2 every where