even with a constant learning rate, CGD succeeds with all these stepsize choices to approximate the main features of the target distribution. In fact, throughout our experiments we *never* saw CGD diverge. In order to measure the convergence speed more quantitatively, we next consider a nonconvex matrix estimation problem, measuring computational complexity in terms of the number of gradient computations performed. We observe that all methods show improved speed of convergence for larger stepsizes, with CGD roughly matching the convergence speed of optimistic gradient descent [@daskalakis2017training], at the same stepsize. However, as we increase the stepsize, other methods quickly start diverging, whereas CGD continues to improve, thus being able to attain significantly better convergence rates (more than two times as fast as the other methods in the noiseless case, with the ratio increasing for larger and more difficult problems). For small stepsize or games with weak interactions on the other hand, CGD automatically invests less computational time per update, thus gracefully transitioning to a cheap correction to GDA, at minimal computational overhead. We believe that the robustness of CGD makes it an excellent candidate for the fast and simple training of machine learning systems based on competition, hopefully helping them 