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On the Nash equilibrium of moment-matching GANs for stationary Gaussian processes

arXiv 2203.07136 ↗First posted 14 Mar 2022stat.ML cs.GT cs.LGcited by 0

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Abstract (arXiv)

Generative Adversarial Networks (GANs) learn an implicit generative model from data samples through a two-player game. In this paper, we study the existence of Nash equilibrium of the game which is consistent as the number of data samples grows to infinity. In a realizable setting where the goal is to estimate the ground-truth generator of a stationary Gaussian process, we show that the existence of consistent Nash equilibrium depends crucially on the choice of the discriminator family. The discriminator defined from second-order statistical moments can result in non-existence of Nash equilibrium, existence of consistent non-Nash equilibrium, or existence and uniqueness of consistent Nash equilibrium, depending on whether symmetry properties of the generator family are respected. We further study empirically the local stability and global convergence of gradient descent-ascent methods towards consistent equilibrium.

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References · 21

  1. 2022Generative Adversarial Networkscited by 5,603
  2. 2018Large Scale GAN Training for High Fidelity Natural Image Synthesiscited by 2,609
  3. 2015Generative Moment Matching Networkscited by 252
  4. 2017Generalization and Equilibrium in Generative Adversarial Nets (GANs)cited by 165
  5. 2015Training generative neural networks via Maximum Mean Discrepancy optimizationcited by 149
  6. 2018The Mechanics of n-Player Differentiable Gamescited by 118
  7. 2017The Numerics of GANscited by 104
  8. 2018The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimizationcited by 98
  9. 2018Last-Iterate Convergence: Zero-Sum Games and Constrained Min-Max Optimizationcited by 97
  10. 2018How Well Generative Adversarial Networks Learn Distributionscited by 78
  11. 2017Gradient descent GAN optimization is locally stablecited by 65
  12. 2019On Finding Local Nash Equilibria (and Only Local Nash Equilibria) in Zero-Sum Gamescited by 35
9 more
  1. 2019On Solving Minimax Optimization Locally: A Follow-the-Ridge Approachcited by 34
  2. 2017Approximation and Convergence Properties of Generative Adversarial Learningcited by 28
  3. 2018Approximability of Discriminators Implies Diversity in GANscited by 28
  4. 2019A Closer Look at the Optimization Landscapes of Generative Adversarial Networkscited by 25
  5. 2020Training Generative Adversarial Networks by Solving Ordinary Differential Equationscited by 21
  6. 2020Towards a Better Global Loss Landscape of GANscited by 17
  7. 2019SGD Learns One-Layer Networks in WGANscited by 16
  8. 2019Maximum Entropy Models from Phase Harmonic Covariancescited by 13
  9. 2020Gradient Descent-Ascent Provably Converges to Strict Local Minmax Equilibria with a Finite Timescale Separationcited by 10

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