## 6 Experiments  
We conducted a series of experiments in a simulated environment to validate our approach. We designed six scenarios in which multiple robots must simultaneously navigate to their designated goal positions without colliding. To emphasize the versatility of our approach in handling environments with varying number of actors, each scenario was executed with two, three, and four controlled robots, respectively. The scenario setup is depicted in Figure 7, illustrating the starting positions, headings, and goal positions of the four robots. The same setup was used for experiments involving fewer robots. Each experiment was repeated 20 times. While the learned model policy is deterministic, the simulation is not due to the imprecise timing of message exchanges. As a result, each run yielded in a slightly different trajectory. This feature enabled us to evaluate the generalizability and adaptivity of our proposed method. To refer conveniently to our method, we coined the name you are not alone (YANA). To compare YANA, we performed a direct comparison with an ablated neural network architecture similar to those used in [15; 40], where a neural network is trained for mobile robot navigation in unknown environments. We implemented the network architecture in a manner consistent with the referenced papers, with CELU activation layers to align them with our approach. We trained this neural network in the same conditions as YANA, employing the same bootstrapping methods and environment setup. This network model was also trained in a shared environment, simultaneously collecting trajectories from three robots. As this method was trained in a shared environment but lacked an information exchange between scene actors, we denote it as you are (not) alone (YA(n)A). Given that learned behaviors in shared environments might also exhibit interaction patterns, we further validate the results against the standard TD3 implementation. In this case, network training was conducted with static obstacles and a single robot in the scene, while retaining the same training setup otherwise. The best-performing performing models after 100 epochs of training were compared for each experiment scenario. All robots in the experimental setup were controlled by their respective policies. As evaluation metrics, we computed the average combined distance traveled, the average combined number of steps and the average collisions, along with their respective standard deviations for each experiment setting. The unit of distance is expressed in meters.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**Training Parameters**} \\ \hline
**Parameter** & **Value** & **Metric** \\ \hline \(\gamma\) & 0.99 & - \\ Batch size & 60 & - \\ Soft target update variable & 0.005 & - \\ Policy noise & 0.2 & - \\
**Root Parameters**: & & \\ \(v_{max}\) & 0.5 & m/s \\ \(v_{min}\) & 0 & m/s \\ \(\omega_{max}\) & 1 & r/s \\ \(\omega_{min}\) & \(-1\) & r/s \\
**Bootstrapping Parameters**: & & \\ p & 0.1 & - \\ Starting max goal distance & 1.5 & m \\ Final max goal distance & 4.5 & m \\ Max goal distance increment & 0.1 & m \\ Starting Gaussian noise & 1 & - \\ variance & 0.1 & - \\ Gaussian noise variance & 0.0001 & - \\ decrement & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: \(Cont.\)