论文标题
$α$ - gan：收敛和估计保证
$α$-GAN: Convergence and Estimation Guarantees
论文作者
论文摘要
我们证明，一般CPE损耗函数gan的最小值优化与关联的$ f $ diverences的最小化之间是双向对应关系。然后，我们专注于$α$ gan，通过$α$ -LOSS定义，该$ loss插入了几个gans（Hellinger，Vanilla，Total变化），并且对应于Arimoto Divergence的最小化。我们表明，对于所有$α$ gan诱导的Arimoto Diverencence，对于所有$α\ in \ Mathbb {r} _ {> 0} \ cup \ {\ infty \} $。但是，在受限制的学习模型和有限样本下，我们提供估计界限，表明各种gan行为与$α$的函数。最后，我们在玩具数据集中介绍了经验结果，该数据集强调了调整$α$超参数的实际实用性。
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 $α\in \mathbb{R}_{>0}\cup\{\infty\}$. However, under restricted learning models and finite samples, we provide estimation bounds which indicate diverse GAN behavior as a function of $α$. Finally, we present empirical results on a toy dataset that highlight the practical utility of tuning the $α$ hyperparameter.
