In an effort to address the training instabilities of GANs, we introduce a class of dual-objective GANs with different value functions (objectives) for the generator (G) and discriminator (D). In particular, we model each objective using $\alpha$-loss, a tunable classification loss, to obtain $(\alpha_D,\alpha_G)$-GANs, parameterized by $(\alpha_D,\alpha_G)\in [0,\infty)^2$. For sufficiently large number of samples and capacities for G and D, we show that the resulting non-zero sum game simplifies to minimizing an $f$-divergence under appropriate conditions on $(\alpha_D,\alpha_G)$. In the finite sample and capacity setting, we define estimation error to quantify the gap in the generator's performance relative to the optimal setting with infinite samples and obtain upper bounds on this error, showing it to be order optimal under certain conditions. Finally, we highlight the value of tuning $(\alpha_D,\alpha_G)$ in alleviating training instabilities for the synthetic 2D Gaussian mixture ring and the Stacked MNIST datasets.

翻译：为了努力解决GANs的培训不稳定问题,我们为发电机(G)和导师(D)引入了一类具有不同价值功能(目标)的双重目标GAN(双重目标)类别。特别是,我们用(alpha_D, alpha_G)$-GAN(以$(alpha_D,\alpha_G)_G)为基准,以[0,\inty]=2美元为基准,对每个目标都采用一种具有不同价值功能(目标)的双重目标GAN(双重目标)。对于数量足够多的G和D的样本和能力,我们表明所产生的非零和游戏简化了在适当条件下以(alpha_D,\alpha_G)$(金枪鱼分类损失)为基准,以获得(alpha_D)$(alpha_G)-GAN(G)$(美元)为基准,我们界定了估计错误,以量化发电机性能与无穷的样本最佳环境相比的差距,并获得关于这一错误的上限,表明在某些条件下要达到最佳秩序。最后,我们强调在合成数据稳定中调整美元(alphax_D_D)和GAGal_GASregregregest Stabiment Staldaldddaldaldaldddald的数据的价值。</s>