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Despite remarkable empirical success, the training dynamics of generativeadversarial networks (GAN), which involves solving a minimax game usingstochastic gradients, is still poorly understood. In this work, we analyzelast-iterate convergence of simultaneous gradient descent (simGD) and itsvariants under the assumption of convex-concavity, guided by a continuous-timeanalysis with differential equations. First, we show that simGD, as is,converges with stochastic sub-gradients under strict convexity in the primalvariable. Second, we generalize optimistic simGD to accommodate an optimismrate separate from the learning rate and show its convergence with fullgradients. Finally, we present anchored simGD, a new method, and showconvergence with stochastic subgradients.

ODE Analysis of Stochastic Gradient Methods with Optimism and Anchoring for Minimax Problems