## 4 Results and Discussion
### Bayesian Optimization Experiments Results  
Our search space reduction effort based on the assumptions described previously drastically reduced the search space to 144 configurations. However, although the search space becomes computationally more affordable, the aim of BO algorithms is not to explore all the hyperparameter configurations. In fact, unlike brute force algorithms such as grid search, we are trying to find the best configurations in a limited number of experiments, as shown in Table 3. We performed 64 BO experiments for a total uninterrupted computing time of 22 h, as illustrated in Figure 6. For the Hyperband early stopping mechanism, we used a maximum allocated resource value R = 27, such as one epoch is equal to one allocated resource. This parameter is set according to our previous experience, where an increase in IoU was observed in the range of the 25 th epochs. In addition, we set s = 2, which corresponds to two brackets of the Successive Halving (SH) algorithm. Thus, the SH algorithm will discard one-third (\(\eta\) = 3) of unpromising experiments in the following bands \([\frac{27}{3},\ \frac{27}{9}]\) (i.e., ninth and third epochs). Thanks to our hyperparameter optimization strategy, 24.6% of configurations with a validation IoU above 0.50 and a validation F1-score over 0.66 were identified. Furthermore, the Hyperband early stopping mechanisms identify 18% of unpromising training experiments by tracking, in a resource-based manner, the validation IoU in regard to runtime for the best previous experiments. In that way, unpromising trials are generally identified early, in the range of 2 min to 4 min after the experiments start. Figure 6: Parallel coordinate plots of hyperparameter optimization experiments. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Optimizer** & **Epochs** & **Batch Size** & \(\boldsymbol{\alpha}\) & \(\mathbf{s}\) & \(\mathbf{R}\) & \(\eta\) \\ \hline Adamax, Adam, RMSprop & [30, 40, 50, 60] & [2; 4; 8; 16; 32; 64] & [\(1\times 10^{-3};1\times 10^{-4}\)] & 2 & 27 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Hyperparameter reduced search space. The best hyperparameter configuration led to a validation IoU of 0.52 and a validation F1-score of 0.68 for a training time of 22 min 38 s. Although the BO algorithm quickly finds the best hyperparameter configurations, understanding the effects of training parameters and optimizer choices is essential from an engineering perspective. That is why we investigated several training configurations. The best/worst experimental results for each hyperparameter configuration explored by the algorithm are shown in Table 4.  
As the selection of hyperparameter configurations is automatically computed by the BO algorithm, some experiments are missing a rigorous quantitative comparison. Thus, our study should be seen as a first qualitative attempt of hyperparameter configuration analysis of DGW image segmentations. The Adamax optimizer configuration represents 7.8% of the experiments which have been the least explored one by the algorithm: it counts a total of five trials and one failed by Hyperband early stopping. This small experimental group led to acceptable segmentation performances. In fact, 66% of this group led to a validation IoU between 0.48 and 0.50. In addition, the batch size tends to have a linear effect on the runtime. Indeed, a decrease of 50% of the batch size led to an average half augmentation of validation IoU and F1-score. Furthermore, decreasing the learning rate coefficient alpha with epoch number seems to confer acceptable performances. Opposite to Adamax, the Adam optimizer category has been the most explored by the algorithm, representing around 53.1% of the experiments. It counts around 26% of hyperparameter configurations with a validation IoU above 0.5 and 8.8% of failed experiments. However, with this optimizer, increasing the epoch number and batch size seems to reduce the segmentation performance and training stability.