Training Generative Adversarial Networks via Primal-Dual Subgradient Methods: A Lagrangian Perspective on GAN
This work addresses mode collapse in GANs for generative modeling, offering a theoretical and practical improvement over standard methods like Wasserstein GAN, though it appears incremental as it builds on existing optimization frameworks.
The paper tackles the problem of mode collapse in generative adversarial networks (GANs) by reformulating GAN training as a convex optimization problem using primal-dual subgradient methods, resulting in a novel objective function that resolves mode collapse in a toy example and demonstrates improved performance on synthetic and real-world image datasets.
We relate the minimax game of generative adversarial networks (GANs) to finding the saddle points of the Lagrangian function for a convex optimization problem, where the discriminator outputs and the distribution of generator outputs play the roles of primal variables and dual variables, respectively. This formulation shows the connection between the standard GAN training process and the primal-dual subgradient methods for convex optimization. The inherent connection does not only provide a theoretical convergence proof for training GANs in the function space, but also inspires a novel objective function for training. The modified objective function forces the distribution of generator outputs to be updated along the direction according to the primal-dual subgradient methods. A toy example shows that the proposed method is able to resolve mode collapse, which in this case cannot be avoided by the standard GAN or Wasserstein GAN. Experiments on both Gaussian mixture synthetic data and real-world image datasets demonstrate the performance of the proposed method on generating diverse samples.