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.
翻译:我们证明一般CPE损失函数的微量优化 GAN 和 相关 $f-diverences 之间的双向对应关系。 然后我们关注 $\ alpha$-GAN, 通过 $\ alpha$- loss 来定义, 将若干 GAN( Herlinger, Vanilla, 全部变化) 相匹配, 与 Arimoto 差异最小化相对应。 我们显示, 由 $\ alpha$- GAN 等量引起的 Arimoto 差异, 对所有 $\ alpha\ in\ mathbb{R ⁇ 0 ⁇ cup ⁇ ⁇ infty ⁇ $ 。 然而, 在 限制学习模式和有限样本下, 我们提供的估计界限显示, 不同的 GAN 行为是 $\ alpha 的函数 。 最后, 我们在一个微量数据集上提出实证结果, 突出调 $\ 超参数的实际效用 。