ODE Analysis of Stochastic Gradient Methods with Optimism and Anchoring for Minimax Problems and GANsDownload PDF

25 Sep 2019 (modified: 24 Dec 2019)ICLR 2020 Conference Blind SubmissionReaders: Everyone
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  • Keywords: GAN, minimax problems, stochastic gradients
  • TL;DR: Convergence proof of stochastic sub-gradients method and variations on convex-concave minimax problems
  • Abstract: Despite remarkable empirical success, the training dynamics of generative adversarial networks (GAN), which involves solving a minimax game using stochastic gradients, is still poorly understood. In this work, we analyze last-iterate convergence of simultaneous gradient descent (simGD) and its variants under the assumption of convex-concavity, guided by a continuous-time analysis with differential equations. First, we show that simGD, as is, converges with stochastic sub-gradients under strict convexity in the primal variable. Second, we generalize optimistic simGD to accommodate an optimism rate separate from the learning rate and show its convergence with full gradients. Finally, we present anchored simGD, a new method, and show convergence with stochastic subgradients.
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