Adaptive Gradient Penalty for Wasserstein GANs: Theory and Applications

Joseph Tafataona Mtetwa (), Kingsley A. Ogudo and Sameerchand Pudaruth
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Joseph Tafataona Mtetwa: Department of Electrical and Electronics Engineering, University of Johannesburg, Johannesburg 2006, South Africa
Kingsley A. Ogudo: Department of Electrical and Electronics Engineering, University of Johannesburg, Johannesburg 2006, South Africa
Sameerchand Pudaruth: ICT Department, Faculty of Information, Communication and Digital Technologies, University of Mauritius, Mauritius

Mathematics, 2025, vol. 13, issue 16, 1-28

Abstract: Wasserstein Generative Adversarial Networks (WGANs) have gained significant attention due to their theoretical foundations and effectiveness in generative modeling. However, training stability remains a major challenge, typically addressed through fixed gradient penalty (GP) techniques. In this paper, we propose an Adaptive Gradient Penalty (AGP) framework that employs a Proportional–Integral (PI) controller to adjust the gradient penalty coefficient λ t based on real-time training feedback. We provide a comprehensive theoretical analysis, including convergence guarantees, stability conditions, and optimal parameter selection. Experimental validation on MNIST and CIFAR-10 datasets demonstrates that AGP achieves an 11.4% improvement in FID scores on CIFAR-10 while maintaining comparable performance on MNIST. The adaptive mechanism automatically evolves penalty coefficients from 10.0 to 21.29 for CIFAR-10, appropriately responding to dataset complexity, and achieves superior gradient norm control with only 7.9% deviation from the target value compared to 18.3% for standard WGAN-GP. This work represents the first comprehensive investigation of adaptive gradient penalty mechanisms for WGANs, providing both theoretical foundations and empirical evidence for their advantages in achieving robust and efficient adversarial training.

Keywords: Wasserstein GANs; adaptive gradient penalty; feedback control; generative modeling; time-series data; convergence analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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