Applications Of Optimal Transport Theory In Generative Adversarial Networks

Since generative Adversarial Nets(GAN)was proposed in 2014,many relevant researchers have paid attention to it and GAN quickly became a mainstream subject in deep learning.The main idea of GAN is to build a generator and a discriminator,and then let the two play a zero-sum game.When the training process reaches a Nash equilibrium,the distribution of the generator equals the real distribution.The optimal transport theory stems from the Monge problem which aims to find a map that can transport a probability distribution to another and minimize transport costs at the same time.But it seems to be pathological.Until the 1940s,Kantorovich generalized the Monge problem,and given the existence and uniqueness of the solution of such prob-lems under specific conditions.The image generation essentially means that let the generator learn the real data distribution from original pictures and use it to generate images close to the real ones.Actually,the optimal transport theory studies transport plans between two different distributions,so we can simply regard the generator and the real image data as two distributions in a high-dimensional space.As long as we find a target function that can quantitatively describe the "distance" between the two distributions,the general optimization methods can be used to train the model.