标题： $α$-GAN：收敛和估计保证 显示英文标题

标题： $α$-GAN: Convergence and Estimation Guarantees

摘要： 我们证明了广义CPE损失函数GAN的极小极大优化与相关$f$-散度最小化之间的双向对应关系。我们随后关注通过$\alpha$-损失定义的$\alpha$-GAN，该方法插值几种GAN（Hellinger，普通，总变分），并对应于Arimoto散度的最小化。我们表明，由$\alpha$-GAN引起的Arimoto散度对于所有$\alpha\in \mathbb{R}_{>0}\cup\{\infty\}$都等价收敛。然而，在受限学习模型和有限样本下，我们提供了估计边界，这些边界表明GAN行为作为$\alpha$的函数而有所不同。最后，我们在一个玩具数据集上展示了调整$\alpha$超参数的实用性的实证结果。 显示英文摘要

摘要： 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.