A unifying $\alpha$-parametrized generator loss function is introduced for a dual-objective generative adversarial network (GAN), which uses a canonical (or classical) discriminator loss function such as the one in the original GAN (VanillaGAN) system. The generator loss function is based on a symmetric class probability estimation type function, $\mathcal{L}_\alpha$, and the resulting GAN system is termed $\mathcal{L}_\alpha$-GAN. Under an optimal discriminator, it is shown that the generator's optimization problem consists of minimizing a Jensen-$f_\alpha$-divergence, a natural generalization of the Jensen-Shannon divergence, where $f_\alpha$ is a convex function expressed in terms of the loss function $\mathcal{L}_\alpha$. It is also demonstrated that this $\mathcal{L}_\alpha$-GAN problem recovers as special cases a number of GAN problems in the literature, including VanillaGAN, Least Squares GAN (LSGAN), Least $k$th order GAN (L$k$GAN) and the recently introduced $(\alpha_D,\alpha_G)$-GAN with $\alpha_D=1$. Finally, experimental results are conducted on three datasets, MNIST, CIFAR-10, and Stacked MNIST to illustrate the performance of various examples of the $\mathcal{L}_\alpha$-GAN system.

翻译：针对采用经典判别器损失函数（如原始GAN系统中的VanillaGAN）的双目标生成对抗网络（GAN），本文引入了一种统一的α参数化生成器损失函数。该生成器损失函数基于对称类概率估计型函数$\mathcal{L}_\alpha$，相应的GAN系统称为$\mathcal{L}_\alpha$-GAN。研究证明，在最优判别器条件下，生成器的优化问题等价于最小化Jensen-$f_\alpha$散度——这是Jensen-Shannon散度的自然推广，其中$f_\alpha$为由损失函数$\mathcal{L}_\alpha$表达的凸函数。同时验证了该$\mathcal{L}_\alpha$-GAN问题可退化为文献中多种GAN问题的特例，包括VanillaGAN、最小二乘GAN（LSGAN）、最小k阶GAN（L$k$GAN）以及近期提出的$(\alpha_D,\alpha_G)$-GAN（当$\alpha_D=1$时）。最后，在MNIST、CIFAR-10和Stacked MNIST三个数据集上进行了实验，展示了$\mathcal{L}_\alpha$-GAN系统各类实例的性能表现。