2022/05/12 by Gowtham R. Kurri, Monica Welfert, Kurri, Gowtham R. +5 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Adversarial Robustness in Machine Learning #FOS: Computer and information sciences #Information Theory (cs.IT) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical Mechanics and Entropy #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2205.06393
openalex publication_date 2022/05/12 · openalex created_date 2022/05/22 · openalex updated_date 2026/07/28
We prove a two-way correspondence between the min-max optimization of general CPE loss function GANs and the minimization of associated f-divergences. We then focus on α-GAN, defined via the α-loss, which interpolates several GANs (Hellinger, vanilla, Total Variation) and corresponds to the minimization of the Arimoto divergence. We show that the Arimoto divergences induced by α-GAN equivalently converge, for all α∈ ℝ>0∪\∞\. However, under restricted learning models and finite samples, we provide estimation bounds which indicate diverse GAN behavior as a function of α. Finally, we present empirical results on a toy dataset that highlight the practical utility of tuning the α hyperparameter.