Revisiting GAN with Bayes-Optimal Discrimination

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.

Generative Adversarial Networks (GANs) have demonstrated strong performance in generating high-quality synthetic data. However, they are limited by no formal guarantees regarding convergence and the effectiveness of the learning process. In practice, this leads to training instability, mode collapse, and sensitivity to hyperparameters. To address this, we propose EmbeddGAN, a novel adversarial training framework based on a dependence-based objective. Instead of relying on a discriminator that classifies samples as real or fake, EmbeddGAN introduces an embedding network that learns a representation in which statistical dependence between samples and their real/fake labels is maximized, while the generator is trained to minimize this dependence. This objective is implemented using the Gini distance correlation (gCor), which equals zero if and only if the embeddings are statistically independent of the real/fake label. Minimizing this objective therefore encourages real and generated samples to become statistically indistinguishable in the learned embedding space. The embedding network projects both real and generated data into a shared low-dimensional space, where distributional discrepancies can be measured directly through pairwise distances. We adopt a minimax training strategy: the embedding network maximizes the Gini distance correlation (maximizing dependence), while the generator minimizes it (minimizing dependence). Experiments on the MNIST, CIFAR-10, and CelebA datasets demonstrate that EmbeddGAN achieves competitive performance relative to established baselines while exhibiting notably stable training dynamics on the evaluated datasets.

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.