mlsanityData to 7 Oct 2026

α-GAN: Convergence and Estimation Guarantees

arXiv 2205.06393 ↗First posted 12 May 2022cs.LG cs.IT math.ITcited by 5

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Abstract (arXiv)

We prove a two-way correspondence between the min-max optimization of general CPE loss function GANs and the minimization of associated f-divergences. We then focus on α-GAN, defined via the α-loss, which interpolates several GANs (Hellinger, vanilla, Total Variation) and corresponds to the minimization of the Arimoto divergence. We show that the Arimoto divergences induced by α-GAN equivalently converge, for all α∈ ℝ>0cup∞. However, under restricted learning models and finite samples, we provide estimation bounds which indicate diverse GAN behavior as a function of α. Finally, we present empirical results on a toy dataset that highlight the practical utility of tuning the α hyperparameter.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 16 of its 34 references that are in the map. First posted on arXiv 12 May 2022.

Builds on

16 of 34 references.

References · 16

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2016Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networkscited by 541
  3. 2016f-GAN: Training Generative Neural Samplers using Variational Divergence Minimizationcited by 504
  4. 2015Norm-Based Capacity Control in Neural Networkscited by 299
  5. 2017Size-Independent Sample Complexity of Neural Networkscited by 289
  6. 2017Generalization and Equilibrium in Generative Adversarial Nets (GANs)cited by 165
  7. 2015Training generative neural networks via Maximum Mean Discrepancy optimizationcited by 149
  8. 2018How Well Generative Adversarial Networks Learn Distributionscited by 78
  9. 2017On the Discrimination-Generalization Tradeoff in GANscited by 48
  10. 2017Approximation and Convergence Properties of Generative Adversarial Learningcited by 28
  11. 2019A Tunable Loss Function for Robust Classification: Calibration, Landscape, and Generalizationcited by 23
  12. 2019A Tunable Loss Function for Binary Classificationcited by 11
4 more
  1. 2021Realizing GANs via a Tunable Loss Functioncited by 10
  2. 2020Cumulant GANcited by 9
  3. 2018Minimax Estimation of Neural Net Distancecited by 7
  4. 2020Least kth-Order and R'enyi Generative Adversarial Networkscited by 6

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Cited by year

Citing papers per year: 2022: 1; 2023: 3; 2024: 0; 2025: 1.

5 papers.

  1. 2023Addressing GAN Training Instabilities via Tunable Classification Lossescited by 5
  2. 2023A Unifying Generator Loss Function for Generative Adversarial Networkscited by 3
  3. 2023(αD,αG)-GANs: Addressing GAN Training Instabilities via Dual Objectivescited by 2
  4. 2022Classification Utility, Fairness, and Compactness via Tunable Information Bottleneck and R'enyi Measurescited by 1
  5. 2025α-GAN by R'enyi Cross Entropycited by 0