In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

Min-max formulations have attracted great attention in the ML community due to the rise of deep generative models and adversarial methods, and understanding the dynamics of (stochastic) gradient algorithms for solving such formulations has been a grand challenge. As a first step, we restrict to bilinear zero-sum games and give a systematic analysis of popular gradient updates, for both simultaneous and alternating versions. We provide exact conditions for their convergence and find the optimal parameter setup and convergence rates. In particular, our results offer formal evidence that alternating updates converge "better" than simultaneous ones.
We systematically analyze the convergence behaviour of popular gradient algorithms for solving bilinear games, with both simultaneous and alternating updates.

Data augmentation is a useful technique to enlarge the size of the training set and prevent overfitting for different machine learning tasks when training data is scarce. However, current data augmentation techniques rely heavily on human design and domain knowledge, and existing automated approaches are yet to fully exploit the latent features in the training dataset. In this paper we propose  \textit{Parallel Adaptive GAN Data Augmentation}(PAGANDA), where the training set adaptively enriches itself with sample images automatically constructed from Generative Adversarial Networks (GANs) trained in parallel. We demonstrate by experiments that our data augmentation strategy, with little model-specific considerations, can be easily adapted to cross-domain deep learning/machine learning tasks such as image classification and image inpainting, while significantly improving model performance in both tasks. Our source code and experimental details are available at \url{https://github.com/miaojiang1987/k-folder-data-augmentation-gan/}.
We present an automated adaptive data augmentation that works for multiple different tasks. 

We propose a rejection sampling scheme using the discriminator of a GAN to
 approximately correct errors in the GAN generator distribution. We show that
 under quite strict assumptions, this will allow us to recover the data distribution
 exactly. We then examine where those strict assumptions break down and design a
 practical algorithm—called Discriminator Rejection Sampling (DRS)—that can be
 used on real data-sets. Finally, we demonstrate the efficacy of DRS on a mixture of
 Gaussians and on the state of the art SAGAN model. On ImageNet, we train an
 improved baseline that increases the best published Inception Score from 52.52 to
 62.36 and reduces the Frechet Inception Distance from 18.65 to 14.79. We then use
 DRS to further improve on this baseline, improving the Inception Score to 76.08
 and the FID to 13.75.

We use a GAN discriminator to perform an approximate rejection sampling scheme on the output of the GAN generator.