EasyDeepLearn

Write the vanilla GAN's minimax objective.

hard

Answer

  • min⁡G\operatorname{min}_{G} max⁡D\operatorname{max}_{D} Ex[log⁡  D(x)]  +  Ez[log⁡(1  −  D(G(z)))]E_{x}[\operatorname{log}\;D(x)]\; + \;E_{z}[\operatorname{log}(1\; - \;D(G(z)))].
  • D tries to output 1 for real, 0 for fake; G tries to make D output 1 on its fakes.
  • In practice, G is trained with the 'non-saturating' loss  −Ez[log⁡  D(G(z))]\mathrm{loss}\; - E_{z}[\operatorname{log}\;D(G(z))] (stronger gradients when D is confident).
  • WGAN replaces this with a Wasserstein-distance-based loss for better stability.
Check yourself — multiple choice
  • MSE between real and fake
  • min⁡G\operatorname{min}_{G} max⁡D\operatorname{max}_{D} E[log D(x)] + E[log(1 - D(G(z)))] — real vs fake classification game; G uses non-saturating variant
  • Same as cross-entropy on labels
  • GAN has no loss

Vanilla GAN: log D + log(1-D(G(z))) minimax; G uses non-saturating -log D(G(z)).

#losses#gan#generative

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