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Mean Field Game GAN

arXiv 2103.07855 ↗First posted 14 Mar 2021cs.LGcited by 0

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Abstract (arXiv)

We propose a novel mean field games (MFGs) based GAN(generative adversarial network) framework. To be specific, we utilize the Hopf formula in density space to rewrite MFGs as a primal-dual problem so that we are able to train the model via neural networks and samples. Our model is flexible due to the freedom of choosing various functionals within the Hopf formula. Moreover, our formulation mathematically avoids Lipschitz-1 constraint. The correctness and efficiency of our method are validated through several experiments.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 17 of its 30 references that are in the map. First posted on arXiv 14 Mar 2021.

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17 of 30 references.

References · 17

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 6,013
  3. 2017Improved Training of Wasserstein GANscited by 2,235
  4. 2014Conditional Generative Adversarial Netscited by 2,162
  5. 2015Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networkscited by 2,054
  6. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,636
  7. 2016Least Squares Generative Adversarial Networkscited by 1,001
  8. 2017Wasserstein GANcited by 639
  9. 2016Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networkscited by 543
  10. 2016f-GAN: Training Generative Neural Samplers using Variational Divergence Minimizationcited by 506
  11. 2017Towards Principled Methods for Training Generative Adversarial Networkscited by 464
  12. 2017Are GANs Created Equal? A Large-Scale Studycited by 267
5 more
  1. 2014On the relation between optimal transport and Schr"odinger bridges: A stochastic control viewpointcited by 99
  2. 2020Learning Stochastic Behaviour from Aggregate Datacited by 12
  3. 2021Learning High Dimensional Wasserstein Geodesicscited by 10
  4. 2018Algorithm for Hamilton-Jacobi equations in density space via a generalized Hopf formulacited by 2
  5. 2018Constrained dynamical optimal transport and its Lagrangian formulationcited by 1

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