## 6 Conclusions  
This study explored the impact of data corruption, including missing and noisy data, on deep learning performance across two distinct domains: supervised learning with NLP tasks (NLP-SL) and deep reinforcement learning for traffic signal optimization (Signal-RL). Our experiments aimed to provide insights into the relationship between data quality and model performance, the trade-offs of imputation strategies, and the effectiveness of increasing data quantity as a remedy for data corruption. **Key Findings**  
1. **Diminishing Returns in Data-Quality Improvement**: Both NLP-SL and Signal-RL experiments revealed that model performance follows a diminishing return curve as data corruption decreases. The relationship between the model score \(S\) and data corruption level \(p\) is well modeled by the function: \[S=a(1-e^{-\lambda(1-p)})\] where parameter \(a=\frac{S_{0}}{1-e^{-\lambda}}\); and \(S_{0}\) is the model score when corruption ratio \(p=0\). This universal trend emphasizes the importance of balancing data quality and preprocessing efforts. 2. **Data Noise is More Detrimental than Missing Data**: Our results demonstrate that noisy data are significantly more detrimental than missing data, leading to faster performance degradation and increased training instability. This was particularly evident in the reinforcement learning task, where inserting noise caused substantial fluctuations in both training and policy stability. 3. **Trade-offs in Data Imputation**: Imputation methods can restore critical information for missing data but introduce a trade-off by potentially adding noise. The decision to impute depends on the imputation accuracy, the corruption ratio, and the nature of the task. The imputation advantage heatmap highlights two key regions: * Imputation Advantageous Corner: A region where accurate imputation significantly boosts model performance. * Imputation Disadvantageous Edge: A region where imputation noise outweighs its benefits, harming model performance. 4. **Two Types of Tasks Identified**: Tasks are classified into two categories based on their sensitivity to noise:Noise-insensitive tasks: These tasks exhibit gradual performance degradation, with decision boundaries on the heatmap that can be effectively modeled using a sigmoid curve. Noise-sensitive tasks: These tasks exhibit sharp performance drops, with decision boundaries closely approximated by an exponential curve. This behavior is typical in deep reinforcement learning tasks. When only \"general imputation\" is available--as opposed to \"exact imputation\"--the sensitivity to noise tends to be further amplified. 5. **Limits of Enlarging Datasets**: Increasing the dataset size partially mitigates the effects of data corruption but cannot fully recover the lost performance, especially under high noisy levels. Enlarging datasets does not entirely offset the detrimental effects of noisy data. The analysis showed that the number of samples required to achieve a certain performance level increases exponentially with the corruption ratio, confirming the exponential nature of the trade-off between data quality and quantity. 6. **Impact of Data Corruption on Learning Efficiency**: Missing data hampers learning efficiency. To achieve the same performance level (if at all possible), the number of required samples--and hence training time--increases exponentially with the data-missing level. 7. **Empirical Rule on Data Importance**: For traffic signal control tasks, approximately 30% of the data are critical for determining model performance, while the remaining 70% can be lost with minimal impact on performance. This observation provides practical guidance for prioritizing efforts in data collection and preprocessing. Note that the exact number may not apply to other tasks and, for many task, this kind of screening is not feasible. **Implications**  
The insights from this study provide direct implications for designing robust machine learning systems, benefiting both practitioners and researchers.