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

arXiv: https://arxiv.org/abs/2608.10096 · HTML: https://mlsanity.com/paper/2608.10096/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 22 references that are in the map.
- First posted on arXiv 10 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Least Squares Generative Adversarial Networks](https://mlsanity.com/paper/1611.04076/) (2016)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [The Composition Theorem for Differential Privacy](https://mlsanity.com/paper/1311.0776/) (2013)
- [Geometric GAN](https://mlsanity.com/paper/1705.02894/) (2017)
- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [Minimax Weight and Q-Function Learning for Off-Policy Evaluation](https://mlsanity.com/paper/1910.12809/) (2019)
- [A Statistical Framework of Watermarks for Large Language Models: Pivot, Detection Efficiency and Optimal Rules](https://mlsanity.com/paper/2404.01245/) (2024)
- [Limits of Detecting Text Generated by Large-Scale Language Models](https://mlsanity.com/paper/2002.03438/) (2020)
- [Detecting LLM-Generated Text with Performance Guarantees](https://mlsanity.com/paper/2601.06586/) (2026)
- [A Statistical Viewpoint on Differential Privacy: Hypothesis Testing, Representation and Blackwell's Theorem](https://mlsanity.com/paper/2409.09558/) (2024)

## Abstract (arXiv)

Modern data science increasingly gives rise to hypothesis-testing problems that are not naturally formulated in terms of parameters within prespecified statistical models. One important example is the dynamic evaluation of optimization algorithms, where decisions must be made during training about whether further updates remain beneficial or the algorithm should switch to a different phase. This issue is particularly relevant in stochastic min-max optimization. Generative adversarial networks (GANs) provide a canonical example, as their training requires repeated decisions about when to switch between discriminator and generator updates, yet existing methods typically rely on fixed update ratios or heuristic criteria. We formulate this switching problem as sequential hypothesis testing and develop an e-process-based adaptive training procedure. During discriminator updates, one e-process tests the null that the discriminator-induced separation between the empirical data distribution and the generator law remains below a target level. During generator updates, with the discriminator fixed, a second e-process tests the reverse null that this separation remains above a refresh level. Conditional on the observed training sample, we prove that fresh empirical indices and latent draws yield conditional e-values that can be accumulated into e-processes, providing anytime-valid Type I error control under adaptive model updates and data-dependent switching. Across multimodal synthetic distributions and image benchmark datasets, the proposed method matches or outperforms the best fixed-ratio baselines under several widely used GAN objectives.