Deciding When to Switch: E-Processes for Adaptive Minimax Training for Generative Adversarial Nets
Authors: Hyunjoo Kim, Sicheng Wu, Agastya Venkatraman, Guang Lin, Sehwan Kim
Organizations: Department of Statistics, Ewha Womans University · Department of Mathematics, Purdue University · Department of Computer Science, Purdue University
Abstract
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.
In modern GANs, maintaining an Exponential Moving Average (EMA) of the generator's weights is a standard practice, as such an averaged model consistently outperforms the actively trained generator. However, the EMA generator is used for final deployment only and does not influence the training process. To address this missed opportunity, we introduce Self-Distilled GAN (SD-GAN) that employs the EMA generator as a teacher to guide the active generator (student) via perceptual loss. We prove the local asymptotic stability of SD-GAN in the Dirac-GAN setting and show that it dampens the parasitic cycling behavior that plagues the conventional GANs. Empirical evaluations across established architectures and datasets demonstrate that SD-GAN improves the final image quality on several metrics (FID and random-FID in particular), stabilizes the optimization trajectory and provides additional learning guidance that is not trivially correlated with the conventional adversarial loss. It also proves effective for fine-tuning pretrained GAN models.
Semi-supervised generative adversarial networks (SSL-GANs) can exploit large unlabeled datasets while retaining a classifier in the discriminator, but their training is often unstable. This paper proposes a population-based evolutionary training strategy in which discriminator learning is formulated as a multi-objective optimization problem. Instead of aggregating the supervised and unsupervised components of the SSL objective into a single scalar loss, the method maintains a population of discriminators ranked by Pareto dominance, enabling the exploration of different trade-offs between classification accuracy and real/fake discrimination. This formulation aims to improve both roles of SSL-GANs: learning accurate classifiers and training generators capable of producing realistic samples. We analyze several variants, including an elitist strategy and a mono-objective ablation, to assess the role of multi-objective selection. Experiments on MNIST with limited labels show improved training robustness compared to SSL-GAN and CE-SSL-GAN state-of-the-art baselines, while the elitist variant consistently achieves the highest classification accuracy.
Francisco Sedeño, Francisco Chicano, Jamal Toutouh
Physical AI is being successfully applied to data which does not follow the traditional paradigm of independent and identically distributed (i.i.d.) samples. In fact, physical AI is often trained on data which is not random at all, and is instead derived from chaotic dynamical systems like turbulence. We aim to explain the empirical success of these methods using the example of generative adversarial networks (GANs), whose statistical learning theory under the i.i.d. assumption is generally well understood. We prove that it is possible, using an infinite-dimensional model of generative adversarial learning (GAL), to learn the invariant distribution of a sufficiently chaotic dynamical system from a single deterministically evolving time series of its states or measurements thereof, and give explicit rates for the convergence to the solution in terms of the Jensen-Shannon divergence.