  Stochastic min-max optimization has gained interest in the machine learning
community with the advancements in GANs and adversarial training. Although game
optimization is fairly well understood in the deterministic setting, some
issues persist in the stochastic regime. Recent work has shown that stochastic
gradient descent-ascent methods such as the optimistic gradient are highly
sensitive to noise or can fail to converge. Although alternative strategies
exist, they can be prohibitively expensive. We introduce Omega, a method with
optimistic-like updates that mitigates the impact of noise by incorporating an
EMA of historic gradients in its update rule. We also explore a variation of
this algorithm that incorporates momentum. Although we do not provide
convergence guarantees, our experiments on stochastic games show that Omega
outperforms the optimistic gradient method when applied to linear players.
