$α$-GAN: Convergence and Estimation Guarantees

Abstract

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.

Towards Addressing GAN Training Instabilities: Dual-objective GANs with Tunable Parameters

“…Note that (34) is exactly the same bound as that in [30,Equation (35)]. Hence, the remainder of the proof follows from the proof of [30,Theorem 3], where α = α G .…”