  Generative adversarial training (GAT) is a recently introduced adversarial
defense method. Previous works have focused on empirical evaluations of its
application to training robust predictive models. In this paper we focus on
theoretical understanding of the GAT method and extending its application to
generative modeling and out-of-distribution detection. We analyze the optimal
solutions of the maximin formulation employed by the GAT objective, and make a
comparative analysis of the minimax formulation employed by GANs. We use
theoretical analysis and 2D simulations to understand the convergence property
of the training algorithm. Based on these results, we develop an incremental
generative training algorithm, and conduct comprehensive evaluations of the
algorithm's application to image generation and adversarial out-of-distribution
detection. Our results suggest that generative adversarial training is a
promising new direction for the above applications.
