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Recent applications that arise in machine learning have surged significant interest in solving min-max saddle point games. This problem has been extensively studied in the convex-concave regime for which a global equilibrium solution can be computed efficiently. In this talk, we study the problem in the non-convex regime and show that an $\epsilon$--first order stationary point of the game can be computed when one of the player’s objective can be optimized to global optimality efficiently. We discuss the application of the proposed algorithm in defense agains adversarial attacks to neural networks, generative adversarial networks, fair learning, and generative adversarial imitation learning.