We are interested in finding anO(ε)-stationary point of the functionΦ( ) = maxy Yf( ,y). Thisminimax optimization formulation includes manymachine learning applications such as regularized empirical risk minimization [41, 52], AUC maximization [39, 48], robust optimization [14, 46], adversarial training [16, 17, 40] and reinforcement learning [13, 43].

In this supplementary, we provide additional details, results and visualizations.