Deciding When to Switch: E-Processes for Adaptive Minimax Training for Generative Adversarial Nets

GAN training is notoriously unstable, often suffering from vanishing gradients or mode collapse due to the complex, coupled dynamics between the generator and discriminator. While many researchers have focused on modifying loss functions or regularization techniques, the scheduling of updates—deciding when to stop training one network and switch to the other—remains largely heuristic or fixed. This paper asks: can we replace these arbitrary schedules with a statistically rigorous, data-adaptive rule based on sequential hypothesis testing?

The authors formulate the switching problem as a sequential hypothesis test. They define the discriminator's goal as testing whether the separation between the empirical data distribution and the generator's distribution is below a target threshold. Conversely, the generator's goal is to test whether that separation remains above a certain refresh level.

To implement this, the authors utilize e-processes, which are nonnegative processes that provide anytime-valid Type I error control. By constructing e-values from the discriminator's output, the algorithm monitors the training progress in real-time. When the accumulated evidence (the e-process) crosses a predefined threshold, the algorithm automatically triggers a switch to the other network. This ensures that the discriminator is updated only until it provides a useful signal, and the generator is updated only until its progress necessitates a new discriminator perspective.

The proposed method provides a formal, anytime-valid framework for adaptive GAN training. By using conformal e-prediction, the authors ensure that the evidence scores remain valid even when using neural networks that only approximate the true density ratio. Experimental results across multimodal synthetic distributions and standard image benchmarks demonstrate that this adaptive scheduling consistently matches or outperforms traditional fixed-ratio update schedules, providing a more stable and principled training trajectory.