$\alpha$-GAN: Convergence and Estimation Guarantees

• URL: http://arxiv.org/abs/2205.06393v1
• Date: Thu, 12 May 2022 23:26:51 GMT
• Title: $\alpha$-GAN: Convergence and Estimation Guarantees
• Authors: Gowtham R. Kurri, Monica Welfert, Tyler Sypherd, Lalitha Sankar
• Abstract summary: We prove a correspondence between the min-max optimization of general CPE loss function GANs and the minimization of associated $f$-divergences. We then focus on $alpha$-GAN, defined via the $alpha$-loss, which interpolates several GANs and corresponds to the minimization of the Arimoto divergence.
• Score: 7.493779672689531
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\alpha$-GAN, defined via the $\alpha$-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 $\alpha$-GAN equivalently converge, for all $\alpha\in \mathbb{R}_{>0}\cup\{\infty\}$. However, under restricted learning models and finite samples, we provide estimation bounds which indicate diverse GAN behavior as a function of $\alpha$. Finally, we present empirical results on a toy dataset that highlight the practical utility of tuning the $\alpha$ hyperparameter.

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