# Root Cause Attribution of Delivery Risks via Causal Discovery with Reinforcement Learning
## 3 Experiments  
Identifying key factors influencing delivery risk is crucial in supply chain management, and multiple studies have laid the groundwork by focusing on variables that directly impact delivery outcomes. For instance, variables such as **shipment mode** and **delivery status** have consistently been found to influence delays and overall efficiency in supply chains. **shipment mode**, in particular, determines the speed and reliability of deliveries, with studies showing that faster, premium shipping options reduce the likelihood of delays compared to economy modes [17; 24]. Similarly, **delivery status** reflects real-time shipment progress, which has been linked to late delivery risks, as it indicates the presence or absence of disruptions [18].  
Other critical variables commonly examined include **order quantity** and **customer segment**. **Order quantity** can strain logistics if not adequately managed, potentially leading to bottlenecks in shipping [19]. **Customer segment** analysis provides insights into delivery priority and logistical complexity, as certain segments (e.g., corporate clients) often require stricter delivery timelines and tailored services [28]. Additionally, **sales per customer** and **profit ratio** are frequently considered in supply chain studies to determine the financial impact of delayed deliveries and prioritize orders based on revenue potential [23].  
By selecting these proper variables, one can capture a comprehensive set of delivery risk factors identified in prior research (we chose 16 variables in a real experiment in  
\begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt} p{142.3 pt}} \hline \hline
**Parameter** & **Value** & **Description** \\ \hline
**Learning Rate** & 0.001 & Controls the size of the step taken in each iteration during gradient descent. Chosen to ensure stable convergence without overshooting. \\ \hline
**Epochs** & 500 & Number of iterations over the entire dataset during training. Selected based on performance stabilization after cross-validation. \\ \hline
**Batch Size** & 64 & Number of samples processed before the model updates. A moderate size chosen for memory efficiency and gradient accuracy. \\ \hline
**Optimizer** & Adam & Adam optimizer dynamically adjusts learning rates, suited for handling sparse gradients and noisy data in supply chains. \\ \hline
**Regularization (L2)** & \(\lambda=0.0001\) & Prevents overfitting by penalizing large weights. Regularization factor tuned for balance between complexity and generalization. \\ \hline
**Dropout Rate** & 0.2 & Reduces overfitting. A value of 20\% chosen based on experimentation for improved generalization. \\ \hline
**Reward Function Parameters** & \(\lambda_{1}=0.5\), \(\lambda_{2}=0.1\) & Two hyperparameters for reward function: \(\lambda_{1}\) controls the causal reward weight, and \(\lambda_{2}\) is a penalty factor for weak causal links. \\ \hline
**Causal Strength Threshold** & 0.05 & Threshold set to filter out weaker causal links, ensuring only significant relationships are included in the causal graph. \\ \hline \hline \end{tabular}
\end{table}
Table 2: Hyperparameters used in the training process.  
the next section in Table 3). Each variable represents a distinct aspect of delivery risk, from logistical decisions (like shipping mode and scheduled days) to customer-related metrics (such as customer segment and sales). This diverse selection, grounded in existing literature, enables a robust analysis of factors that collectively contribute to delivery risks.