Consistency of Multiagent Distributed Generative Adversarial Networks

The mathematical properties of generative adversarial networks (GANs) are presented via opinion dynamics, in which the discriminator is regarded as an agent while the generator is regarded as the principal (or another type of agent) in a GAN. In some cases, the overall convergence must be achieved through establishing a local information interaction between one agent and its neighbors via the multiagent system consistency theory and algorithms. So the goals of the multiagent consistency algorithm and the Nash equilibrium of GANs are virtually identical. Then, the existence of the Degroot model solution proves that the generator and discriminator in GANs can reach a consensus on the distribution function. Therefore, a new sufficient and necessary condition for the existence of a Nash equilibrium in GANs is obtained. Furthermore, a novel multiagent distributed GAN (MADGAN) is proposed to address the multiagent cognitive consistency problem in large-scale distributed network, based on the social group wisdom and the influence of the network structure on the agent. The nodes of a multiagent network are regarded as discriminators and generators, the discriminator with a relatively large degree of influence as a leader, and the generator as a follower, the lines with the degree denote the influence between the agents. The conditions of consensus are presented for a multigenerator and multidiscriminator (multiagent) distributed GAN by analyzing the existence of stationary distribution to the Markov chain of multiple agent states. Finally, theoretical results are verified with simulation based on the MNIST dataset.