the generative adversarial Nets game does not satisfy the main sufficient condition for convergence so that doesn't mean that they don't converge it means that we don't know whether they converge or not according to you the main criterion that we can look at and it seems like in practice they do converge sometimes and they doubt other times and we don't have a great understanding of why they do or don't but the most important thing under said is that simultaneous gradient descent is not really an algorithm for looking for