## 4 Evaluation Metrics  
This section introduces the evaluation metrics used to assess the performance of DRL-based autonomous driving techniques. These metrics are defined for a given driving episode \(i\) in terms of the travel distance, Route Completion, driving stability, and cumulative reward. * Travel Distance \(D_{travel}^{i}\): The distance traveled by the agent during episode \(i\) is calculated by cumulatively summing the distance covered at each step until the final time step, as illustrated in Figure 3.  
* Route Completion \(C^{i}\): This metric represents the proportion of the intended route \(D_{route}^{i}\), generated from the start to the destination in episode \(i\), that the ego vehicle successfully traveled from the starting point. It is computed according to Equation (32): \[C^{i}=\frac{D_{travel}^{i}}{D_{route}^{i}}.\] (32)
* Speed Mean \(\overline{V}_{ego}^{i}\): This metric denotes the average speed of the ego vehicle over the entire duration of episode \(i\) and is computed as shown in Equation (33). \[\overline{V}_{ego}^{i}=\frac{1}{T_{i}}\sum_{t=1}^{T_{i}}V_{ego}^{i,t}\] (33) where \(V_{ego}^{i,t}\) represents the vehicle's speed at each step \(t\) and \(T_{i}\) denotes the total number of steps in episode \(i\). * Centerline Deviation Mean \(\overline{D}_{center}^{i}\): This metric quantifies how far the vehicle deviates from the lane centerline during driving and is computed according to Equation (34). It is based on the average of the Centerline Deviation values \(D_{center}^{i,t}\) at each time step. A smaller value indicates stable lane keeping, whereas a larger value suggests a higher likelihood of lane departure. \[\overline{D}_{center}^{i}=\frac{1}{T_{i}}\sum_{t=1}^{T_{i}}D_{center}^{i,t}\] (34)
* Episode Reward \(R_{epi}^{i}\): Episode Reward \(R_{epi}^{i}\) represents the total cumulative reward obtained by the agent during episode \(i\) and is computed according to Equation (35). \[R_{epi}^{i}=\sum_{t=1}^{T_{i}}R_{step}^{i,t}.\] (35)
* Episode Reward Mean \(\overline{R}_{epi}\) and Step Reward Mean \(\overline{R}_{step}^{i}\): The average reward metric is defined along two temporal scales. The first is the Episode Reward Mean, which is calculated by summing the total rewards \(R_{epi}^{i}\) obtained across all \(N\) episodes and dividing by the number of episodes. This metric represents the average reward per episode and is computed according to Equation (36). The second is the Step Reward Mean, which is calculated by dividing the total episode reward \(R_{epi}^{i}\) by the total number of steps \(T_{i}\) in episode \(i\). This metric represents the average reward per step and is computed according to Equation (37). \[\overline{R}_{epi}=\frac{1}{N}\sum_{i=1}^{N}R_{epi}^{i},\] (36) \[\overline{R}_{step}^{i}=\frac{1}{T_{i}}\sum_{t=1}^{T_{i}}R_{step}^{i,t}=\frac {1}{T_{i}}R_{epi}^{i}.\] (37)
* Reward Standard Deviation \(\sigma_{R}^{i}\): This metric represents the variability of the rewards obtained by the agent during episode \(i\) and is defined as shown in Equation (38). A lower value indicates that the learned policy is more stable and consistently acquires rewards. \[\sigma_{R}^{i}=\sqrt{\frac{1}{T_{i}}\sum_{t=1}^{T_{i}}\left(R_{step}^{i,t}- \overline{R}_{step}^{i}\right)^{2}}\] (38)* Success Rate \(\bar{\bar{S}}\): For each episode \(i\), the binary success indicator \(S^{i}\) is defined according to Equation (39), which determines whether the ego vehicle successfully reached its destination. In this formulation, an episode is considered successful (\(S^{i}=1\)) if the final vehicle position \((x_{\
u}^{i},y_{\
u}^{i})\) is within 5 m of the goal position \((x_{w}^{i},y_{w}^{i})\). Otherwise, it is considered a failure (\(S^{i}=0\)). The overall Success Rate \(\bar{\bar{S}}\) is then computed by averaging the success indicators across all \(N\) episodes, as defined in Equation (40). \[S^{i}= \begin{cases}1,&\text{if }\sqrt{(x_{v}^{l}-x_{w}^{l})^{2}+(y_{v}^{l}-y_ {w}^{l})^{2}}<5\\ 0,&\text{otherwise},\end{cases}