Convergence of Non-Convex Non-Concave GANs Using Sinkhorn Divergence

Sinkhorn divergence is a symmetric normalization of entropic regularized optimal transport. It smooth and continuous metrized weak-convergence with excellent geometric properties. We use it as an alternative for the minimax objective function in formulating generative adversarial networks. The optimization defined objective, under non-convex non-concave condition. This work focuses on optimization’s convergence stability. propose first order sequential stochastic gradient descent ascent (SeqSGDA) algorithm. Under some mild approximations, learning converges to local points. Using structural similarity index measure (SSIM), we supply non-asymptotic analysis algorithm’s rate. Empirical evidences show rate, which inversely proportional number iterations, when tested tiny colour datasets Cats CelebA deep convolutional networks ResNet neural architectures. entropy regularization parameter $\varepsilon $ approximated SSIM tolerance $\epsilon . determine that iteration complexity return -stationary point be $\mathcal {O}\left ({\kappa \, \log (\epsilon ^{-1})}\right)$ , where $\kappa value depends divergence’s convexity step ratio SeqSGDA