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.

引入了一种统一的α参数化生成器损失函数，用于一种双目标生成对抗网络（GAN），其使用经典鉴别器损失函数，例如原始GAN（VanillaGAN）系统中的损失函数。生成器损失函数基于对称类概率估计类型函数L_α，得到的GAN系统称为L_α-GAN。在最优鉴别器下，证明了生成器的优化问题包括最小化Jensen-f_α-分歧，这是Jensen-Shannon分歧的自然推广，其中f_α是用损失函数L_α表示的凸函数。还证明了这个L_α-GAN问题作为文献中一些GAN问题的特例，包括VanillaGAN、最小二乘GAN（LSGAN）、最小k阶GAN（LkGAN）和最近引入的（αD，αG）-GAN（其中αD=1）。最后，在三个数据集MNIST、CIFAR-10和Stacked MNIST上进行实验，以说明各种示例的L_α-GAN系统的性能。

生成对抗网络统一生成器损失函数