Understanding GANs: the LQG Setting
This work addresses fundamental issues in GANs for researchers, but it is incremental as it focuses on a simplified benchmark.
The paper tackled the problem of understanding and improving GANs in a simple high-dimensional Gaussian setting, where existing architectures often fail due to stability, approximation, and generalization issues, and proposed a new GAN architecture that recovers the maximum-likelihood solution with fast generalization.
Generative Adversarial Networks (GANs) have become a popular method to learn a probability model from data. In this paper, we aim to provide an understanding of some of the basic issues surrounding GANs including their formulation, generalization and stability on a simple benchmark where the data has a high-dimensional Gaussian distribution. Even in this simple benchmark, the GAN problem has not been well-understood as we observe that existing state-of-the-art GAN architectures may fail to learn a proper generative distribution owing to (1) stability issues (i.e., convergence to bad local solutions or not converging at all), (2) approximation issues (i.e., having improper global GAN optimizers caused by inappropriate GAN's loss functions), and (3) generalizability issues (i.e., requiring large number of samples for training). In this setup, we propose a GAN architecture which recovers the maximum-likelihood solution and demonstrates fast generalization. Moreover, we analyze global stability of different computational approaches for the proposed GAN optimization and highlight their pros and cons. Finally, we outline an extension of our model-based approach to design GANs in more complex setups than the considered Gaussian benchmark.