## 2 Background
Some works are concentrated on preemptively predicting the potential error rate for the classifier based on the uncertainty [20] and imbalance [21] of input data. The preemptive extraction and analysis of datasets' meta-features allow this approach to improve Algorithm selection recommendations. The extensive analysis of classification performance on different datasets revealed that in some cases the imbalance of the training dataset may improve the resulting classification accuracy. The paper [22] analyzes the optimization dynamics of Generative Adversarial Network (GAN), focusing on gradient descent updates for both the generator and discriminator. The authors show that while GAN optimization is not a convex-concave game, equilibrium points in traditional GANs remain locally stable under certain conditions. In contrast, Wasserstein GANs (WGANs) can exhibit non-convergent limit cycles near equilibrium. To address these stability issues, the paper proposes a regularization term that improves local stability, accelerates convergence, and mitigates mode collapse. The work [23] investigates the quality of conventional evaluation techniques for measuring GAN performance, such as the Inception Score and Frechet Inception Distance. The authors propose two additional evaluation techniques. The proposed GAN-train technique evaluates the diversity and realism of a GAN's generated images by training a classifier on synthetic images and testing it on real ones, assessing how well the learned distribution matches the target distribution. In contrast, the proposed GAN-test technique measures the classifier's performance when trained on real images and tested on generated ones, capturing the fidelity of the synthetic data. The results demonstrate that these evaluation methods complement existing ones and, when used together, provide a more comprehensive assessment of GAN performance. The study [24] explores the applicability of synthetic images from text-to-image models for image recognition tasks, focusing on zero-shot, few-shot learning, and large-scale model pretraining. The authors find that synthetic data significantly improve classification accuracy in zero-shot settings and remain beneficial in few-shot scenarios, though domain gaps pose challenges. They propose strategies like diversified text prompts and real-image-guided generation to enhance effectiveness. Additionally, synthetic data prove highly effective for model pretraining, sometimes surpassing ImageNet pretraining, particularly for architectures based on Vision Transformers. The study highlights both the potential and limitations of synthetic data, encouraging further research in this area. The authors of [25] use hidden Markov models and regression models to generate synthetic time-series data based on a real smart-home dataset. As part of their research, they investigated a problem of generating the synthetic data from a small amount of real-world samples. Their results show that training Algorithms on a combination of a small real data sample and the synthetic data generated from it can achieve significantly higher activity recognition accuracy than training on the small real data sample alone. Despite extensive research in both Algorithm selection and synthetic data generation, no prior work has explored the use of synthetically generated data for training Algorithm selectors. Algorithm selection has been widely studied across various domains, demonstrating improvements in classification accuracy and efficiency, while synthetic data generation has shown promise in augmenting training datasets, improving model performance, and reducing reliance on large real-world datasets. However, the potential of leveraging synthetic data to enhance the training process of Algorithm selectors remains unexplored. This gap in the literature suggests an opportunity to investigate whether synthetic data can improve the generalization and robustness of Algorithm selection models, particularly in cases where real-world training data are scarce or expensive to obtain.