## 2 Related Work
### Data Imputation Techniques  
Data imputation aims to recover missing information, and various strategies have been proposed. [PERSON] et al. [2] provide a comprehensive review of missing data in machine learning, classifying imputation methods into several categories: simple imputation, regression-based imputation, hot-deck imputation, the Expectation-Maximization (EM) method, multiple imputation, and machine learning-inspired techniques such as k-nearest neighbors (KNN), support vector machines (SVM), decision trees, clustering-based imputation, and ensemble methods. In a more recent taxonomy, [PERSON] et al. [18] group imputation approaches into four main types: statistical, machine learning-based, neural network-based, and optimization-based methods.  
**Statistical Methods**: These include simple approaches like mean, mode, or median imputation [19], as well as more sophisticated techniques like regression imputation and multiple imputation [20]. While straightforward, these methods may introduce bias or underestimate variability.  
**Machine Learning Methods**: Techniques such as k-nearest neighbors (KNN) imputation [21], decision tree-based imputation [22], and Random Forest imputation [23] leverage patterns in data to predict missing values. These methods often outperform simple statistical approaches by capturing complex nonlinear relationships in the data.  
**Deep Learning-based Imputation**: Autoencoders and Generative Adversarial Networks (GANs) have emerged as powerful tools for data imputation. Denoising autoencoders reconstruct inputs with noisy values [24], while GANs generate plausible synthetic data to fill gaps [25]. [PERSON] et al. (2021) [26] used masked language models (e.g., BERT) to impute missing tokens in text data.  
For many applications, particularly LLM pre-training, masking missing data are often sufficient. [PERSON] et al. (2018) showed that masking missing time-series data combined with recurrent neural networks (e.g., GRU) can effectively handle missing data [27]. We summarize common imputation methods, their strengths and weaknesses, and use cases in Table 1.  
**Key Research Gaps**  
While many studies address specific aspects of corrupted data handling, key questions remain unanswered:  
* **Impact of Data Corruption**: What is the quantitative relationship between data corruption ratio and model performance? Can this relationship be consistently modeled across tasks?
* **Effectiveness of imputation**: How do different imputation methods compare in mitigating the effects of missing data? Is it possible to fully restore the utility of corrupted data through imputation?
* **Trade-Off Between Data Quality and Quantity**: Can larger datasets compensate for data corruption? How many additional data are required to offset quality issues and does the marginal utility of additional data diminish with increasing corruption level?  
This study aims to bridge the above gaps by evaluating the effects of data corruption on supervised and reinforcement learning tasks. This study explores the utility of data imputation methods and analyze the trade-off between data quality and quantity, providing insights to guide data collection and preprocessing strategies.