mlsanityData to 7 Oct 2026

Finding Mixed Nash Equilibria of Generative Adversarial Networks

arXiv 1811.02002 ↗First posted 23 Oct 2018cs.LG cs.GT stat.MLcited by 48

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Abstract (arXiv)

We reconsider the training objective of Generative Adversarial Networks (GANs) from the mixed Nash Equilibria (NE) perspective. Inspired by the classical prox methods, we develop a novel algorithmic framework for GANs via an infinite-dimensional two-player game and prove rigorous convergence rates to the mixed NE, resolving the longstanding problem that no provably convergent algorithm exists for general GANs. We then propose a principled procedure to reduce our novel prox methods to simple sampling routines, leading to practically efficient algorithms. Finally, we provide experimental evidence that our approach outperforms methods that seek pure strategy equilibria, such as SGD, Adam, and RMSProp, both in speed and quality.

Key facts. Cited by 48 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Oct 2018.

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Citing papers per year: 2021: 9; 2022: 7; 2023: 8; 2024: 7; 2025: 12; 2026: 5.

48 papers.

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  1. 2021Improving GAN Equilibrium by Raising Spatial Awarenesscited by 22
  2. 2021Derivative-Free Policy Optimization for Linear Risk-Sensitive and Robust Control Design: Implicit Regularization and Sample Complexitycited by 15
  3. 2025Flow Density Control: Generative Optimization Beyond Entropy-Regularized Fine-Tuningcited by 15
  4. 2022An Exponentially Converging Particle Method for the Mixed Nash Equilibrium of Continuous Gamescited by 14
  5. 2023SAN: Inducing Metrizability of GAN with Discriminative Normalized Linear Layercited by 14
  6. 2021Adaptive Importance Sampling meets Mirror Descent: a Bias-variance tradeoffcited by 13
  7. 2022Two-Scale Gradient Descent Ascent Dynamics Finds Mixed Nash Equilibria of Continuous Games: A Mean-Field Perspectivecited by 13
  8. 2025Provable Maximum Entropy Manifold Exploration via Diffusion Modelscited by 12
  9. 2021Complex Momentum for Optimization in Gamescited by 11
  10. 2023Symmetric Mean-field Langevin Dynamics for Distributional Minimax Problemscited by 11
  11. 2022Provably convergent quasistatic dynamics for mean-field two-player zero-sum gamescited by 9
  12. 2021DO-GAN: A Double Oracle Framework for Generative Adversarial Networkscited by 6
36 more
  1. 2021Game of GANs: Game-Theoretical Models for Generative Adversarial Networkscited by 6
  2. 2023Stochastic Re-weighted Gradient Descent via Distributionally Robust Optimizationcited by 6
  3. 2026Verifier-Constrained Flow Expansion for Discovery Beyond the Datacited by 6
  4. 2022Transferable Reward Learning by Dynamics-Agnostic Discriminator Ensemblecited by 5
  5. 2023Wasserstein Gradient Flow over Variational Parameter Space for Variational Inferencecited by 5
  6. 2025Adversarial Training for Defense Against Label Poisoning Attackscited by 5
  7. 2025Expected Variational Inequalitiescited by 5
  8. 2024Analysis of Kernel Mirror Prox for Measure Optimizationcited by 4
  9. 2024Inclusive KL Gradient Flows: Otto-Wasserstein, Fisher-Rao-Gaussian, and Local-Estimator Dynamicscited by 4
  10. 2021On Characterizing GAN Convergence Through Proximal Duality Gapcited by 3
  11. 2024A Fisher-Rao gradient flow for entropic mean-field min-max gamescited by 3
  12. 2021Convergence of GANs Training: A Game and Stochastic Control Methodologycited by 2
  13. 2022Simultaneous Transport Evolution for Minimax Equilibria on Measurescited by 2
  14. 2023PAPAL: A Provable PArticle-based Primal-Dual ALgorithm for Mixed Nash Equilibriumcited by 2
  15. 2025Convergence of two-timescale gradient descent ascent dynamics: finite-dimensional and mean-field perspectivescited by 2
  16. 2025Convergence of Time-Averaged Mean Field Gradient Descent Dynamics for Continuous Multi-Player Zero-Sum Gamescited by 2
  17. 2025Fast 2DGS: Efficient Image Representation with Deep Gaussian Priorcited by 2
  18. 2026A Unified Density Operator View of Flow Control and Mergingcited by 2
  19. 2021WGAN with an Infinitely Wide Generator Has No Spurious Stationary Pointscited by 1
  20. 2023MAT: Mixed-Strategy Game of Adversarial Training in Fine-tuningcited by 1
  21. 2023Sinkhorn Flow: A Continuous-Time Framework for Understanding and Generalizing the Sinkhorn Algorithmcited by 1
  22. 2024Mirror Descent-Ascent for mean-field min-max problemscited by 1
  23. 2025Curriculum-Adapted Robust Reinforcement Learning for UAV Deconfliction in Adversarial Environmentscited by 1
  24. 2025WGAST: Weakly-Supervised Generative Network for Daily 10 m Land Surface Temperature Estimation via Spatio-Temporal Fusioncited by 1
  25. 2026Entropy-Regularized Adjoint Matching for Offline Reinforcement Learningcited by 1
  26. 2022Large deviations for interacting particle dynamics for finding mixed equilibria in zero-sum gamescited by 0
  27. 2022Achieve Optimal Adversarial Accuracy for Adversarial Deep Learning using Stackelberg Gamecited by 0
  28. 2023Towards Optimal Randomized Strategies in Adversarial Example Gamecited by 0
  29. 2024Leveraging Noisy Observations in Zero-Sum Gamescited by 0
  30. 2024Efficient Public Health Intervention Planning Using Decomposition-Based Decision-Focused Learningcited by 0
  31. 2024Double Oracle Neural Architecture Search for Game Theoretic Deep Learning Modelscited by 0
  32. 2025Nested Annealed Training Scheme for Generative Adversarial Networkscited by 0
  33. 2025Meta Policy Switching for Secure UAV Deconfliction in Adversarial Airspacecited by 0
  34. 2025Physics Informed Generative Models for Magnetic Field Imagescited by 0
  35. 2026Local exponential stability of mean-field Langevin descent-ascent and associated particle systemcited by 0
  36. 2026Policy Gradient for Continuous-Time Robust Markov Decision Processescited by 0