text: This paper proposes a simple modification to the standard alternating stochastic gradient method for GAN training, which stabilizes training, by adding a prediction step. This is a clever and useful idea,  and the paper is very well written.  The proposed method is very clearly motivated, both intuitively and mathematically,  and the authors also provide theoretical guarantees on its convergence behavior.  I particularly liked the analogy with the damped harmonic oscillator. The experiments are well designed and provide clear evidence in favor of the usefulness of the proposed technique.  I believe that the method proposed in this paper will have a significant impact in the area of GAN training. I have only one minor question: in the prediction step, why not use a step size, say $\bar{u}_k+1 = u_{k+1} + \gamma_k (u_{k+1} − u_k)$, such that the "amount of predition" may be adjusted?