Hellinger loss function for Generative Adversarial Networks
This work addresses robustness in GAN training for machine learning applications, but it is incremental as it modifies an existing loss function.
The paper tackled the problem of training Generative Adversarial Networks (GANs) by proposing Hellinger-type loss functions, which improved estimation accuracy and robustness under data contamination, as demonstrated in simulations.
We propose Hellinger-type loss functions for training Generative Adversarial Networks (GANs), motivated by the boundedness, symmetry, and robustness properties of the Hellinger distance. We define an adversarial objective based on this divergence and study its statistical properties within a general parametric framework. We establish the existence, uniqueness, consistency, and joint asymptotic normality of the estimators obtained from the adversarial training procedure. In particular, we analyze the joint estimation of both generator and discriminator parameters, offering a comprehensive asymptotic characterization of the resulting estimators. We introduce two implementations of the Hellinger-type loss and we evaluate their empirical behavior in comparison with the classic (Maximum Likelihood-type) GAN loss. Through a controlled simulation study, we demonstrate that both proposed losses yield improved estimation accuracy and robustness under increasing levels of data contamination.