  Minimax problems of the form $\min_x \max_y \Psi(x,y)$ have attracted
increased interest largely due to advances in machine learning, in particular
generative adversarial networks. These are typically trained using variants of
stochastic gradient descent for the two players.
  Although convex-concave problems are well understood with many efficient
solution methods to choose from, theoretical guarantees outside of this setting
are sometimes lacking even for the simplest algorithms.
  In particular, this is the case for alternating gradient descent ascent,
where the two agents take turns updating their strategies.
  To partially close this gap in the literature we prove a novel global
convergence rate for the stochastic version of this method for finding a
critical point of $g(\cdot) := \max_y \Psi(\cdot,y)$ in a setting which is not
convex-concave.
