Adversarial training, a particular case of multi-objective optimization, is an increasingly prevalent machine learning technique: some of its most notable applications include GAN-based generative modeling, adversarial training, and self-play techniques in reinforcement learning applied to complex games such as Go or Poker. In many cases, a \emph{single} pair of networks is typically trained using (stochastic) gradient descent ascent to find an approximate equilibrium of a highly nonconcave-nonconvex minimax problem. In this talk, we will investigate some limitation of unconstrained gradient descent-ascent to understand learning in minimax games.


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