生成对抗网络模型的泛化与均衡研究
摘  要：在互联网时代快速发展的当代，各式各样的数据不断地涌现出来。人们开始考虑如何从大数据中获得对这个世界的认知。生成对抗网络（GAN）以其独特的对抗性训练方式和内涵的机器博弈思维照亮了人工智能发展道路。当然，GAN在训练过程中无法稳定和全局收敛。在众多GAN模型中比较经典的Wasserstein GAN改进了度量数据分布的距离，抛弃了JS散度和KL散度，EM距离的优势特别明显，同时以其独特的目标函数惩罚机制使得训练过程比较稳定。当然在目标函数的角度下，LS-GAN（损失敏感）和GLS-GAN（广义的LS-GAN）的“按需分配的能力”，充分发挥了Lipschitz属性。同时从梯度向量角度来稳定训练过程，零梯度惩罚方法和本文的梯度中心化算法是直接作用在梯度向量上使得GAN的泛化和平衡得到提高。本文将要从目标函数、梯度向量优化和博弈论思维的角度来尝试探究GAN模型训练过程中要达到的纳什均衡状态。
关键词：生成对抗网络；纳什均衡；对抗训练；博弈论思维
Abstract：In the rapid development of the Internet, all kinds of data are constantly emerging. People are starting to think about how they can learn about the world from big data. Generative antagonism network (GAN) illuminates the development path of artificial intelligence with its unique training method of antagonism and machine game thinking. Of course, GAN cannot stabilize and converge globally during training.Among many GAN models, Wasserstein GAN, which is more classical, improves the distance of measurement data distribution, and abandons JS divergence and KL divergence. The advantage of EM distance is particularly obvious.  Meanwhile, it makes the training process more stable with its unique penalty mechanism of target function.Of course, from the perspective of the objective function, the "ability to allocate according to demand" of LS-GAN (loss sensitivity) and GLS-GAN (generalized LS-GAN) gives full play to the Lipschitz attribute.Meanwhile, from the perspective of gradient vector to stabilize the training process, the zero gradient penalty method and the gradient centralization algorithm in this paper directly act on the gradient vector to improve the generalization and equilibrium of GAN. This paper attempts to explore the Nash equilibrium state to be achieved in the training of GAN model from the perspectives of objective function, gradient vector optimization and game theory.
Key words：Generative antagonistic network; Nash equilibrium; adversarial training; Game theory thinking
目录
生成对抗网络模型的泛化与均衡研究 1
1  生成对抗网络（GAN）的纳什均衡研究背景 3
2  GAN模型的几大开放性问题 4
2.1  GAN与其他生成模型的权衡是什么？ 4
2.2  GAN可以模拟哪种分布？ 5
2.3  除了图像合成领域，GAN还适合哪些领域？ 5
2.3.1  文本数据的离散性问题 5
2.3.2  GAN在结构化数据和非结构化数据（如图形）上的应用前景 5
2.3.3  音频领域 5
2.4  GAN是如何保证在训练过程中收敛的？ 5
2.5  GAN与对抗样本有什么联系？ 6
3  Wasserstein GAN、LS-GAN以及GLS-GAN 6
3.1  从正则项了解如何让GAN收敛 6
3.2  标准GAN和其“无限的建模能力”[] 8
3.3  WassersteinGAN和解决梯度消失问题的方法 8
4  梯度角度：Gradient Centralization（梯度中心化算法） 10
4.1  Gradient Centralization（梯度中心化算法）的原理 11
4.1.1  梯度中心化算法研究目的 12
4.1.2  梯度中心化算法基本原理 14
4.1.3  梯度中心化算法在WGAN、LS-GAN和GLS-GAN上的应用 15
4.2  Game Theory（博弈论角度）角度下的泛化能力和纳什均衡 16
5  算法结构和研究结果 16
5.1  算法结构 16
5.2  WGAN-与标准GAN模型结构不同的算法结构 18
6  结论 20
6.1  总结 20
6.2  研究价值和实际应用的展望 21
6.3  研究思想后续和可行性探究 22
参考文献: 23