Generative adversarial networks (GANs) are a class of generative models with two antagonistic neural networks: a generator and a discriminator. These two neural networks compete against each other through an adversarial process that can be modeled as a stochastic Nash equilibrium problem. Since the associated training process is challenging, it is fundamental to design reliable algorithms to compute an equilibrium. In this paper, we propose a stochastic relaxed forward-backward (SRFB) algorithm for GANs and we show convergence to an exact solution when an increasing number of data is available. We also show convergence of an averaged variant of the SRFB algorithm to a neighborhood of the solution when only few samples are available. In both cases, convergence is guaranteed when the pseudogradient mapping of the game is monotone. This assumption is among the weakest known in the literature. Moreover, we apply our algorithm to the image generation problem.
翻译:生成的对抗网络(GANs)是一组基因模型,有两种对立神经网络:一个发源人和一个歧视者。这两个神经网络通过一个可以模拟为随机纳什平衡问题的对抗过程相互竞争。由于相关的培训过程具有挑战性,因此设计可靠的算法以计算平衡至关重要。在本文中,我们提议为GANs设计一种随机放松的前向后向算法(SRFB)算法,当数据数量不断增加时,我们表现出正统的解决方法。我们还显示了SRFB算法的平均变式在只有少数样本可用的情况下与解决方案的邻里相融合。在这两种情况下,当游戏的假基因图绘制为单调时,都会保证趋同。这一假设是文献中已知的最弱的。此外,我们还将我们的算法应用于图像生成问题。