## 4 Results
### Ablation Studies
#### 4.3.1 Ablation Studies: Effects of Automatic Curriculum Learning
With the training progressing, e.g., episodes 50,000 and 100,000, the prediction network suggests an increment in success rate in the regions of favorable initial poses, where the increment also spreads to non-favorable initial pose. In both cases, tasks with \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Relative Orientation**} & \multicolumn{4}{c}{**Average Success Rate**} \\ \cline{2-5}  & _NavACL p.t._ & _RND_ & _NavACL e.t.e._ & **Baseline** \\ \hline \(0^{\circ}\) & **86.6\%** & 58.5\% & 50.3\% & 16.5\% \\ \hline \(-45^{\circ}\) & **93.7\%** & 55.6\% & 25.5\% & 3.3\% \\ \hline \(+45^{\circ}\) & **88.0\%** & 52.2\% & 53.5\% & 5.0\% \\ \hline \(-90^{\circ}\) & **90.5\%** & 43.2\% & 8.9\% & 0\% \\ \hline \(+90^{\circ}\) & 18.5\% & **45.5\%** & 32.0\% & 0\% \\ \hline \(-135^{\circ}\) & **48.2\%** & 36.9\% & 2.2\% & 0\% \\ \hline \(+135^{\circ}\) & 11.9\% & **37.1\%** & 19.8\% & 0\% \\ \hline \(+180^{\circ}\) & 15.7\% & **34.2\%** & 8.0\% & 0\% \\ \hline Mean of \{\(0^{\circ},\pm 45^{\circ},\pm 90^{\circ}\) (Intrapolated Tasks) & **75.5\%** & 51.1\% & 34.1\% & 5.0\% \\ \hline Mean of \{\(\pm 135^{\circ},180^{\circ}\) (Extrapolated Tasks)} & 25.3\% & **36.1\%** & 10.0\% & 0\% \\ \hline Mean of All Orientations & **56.6\%** & 45.4\% & 25.0\% & 3.1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The statistics of testing results are presented. The averaged success rate of reaching the target for each ablation variant and baseline approach are shown. The averaged success rate is calculated as the mean success rates over \(11\times 11\) grid points from Figure 7.  
Figure 8: Two-dimensional interpolation of the success probability estimated by \(f_{\pi}\) at different stages of training, where red areas indicate high success probability estimates and blue areas indicate low success probability estimates. In this case, the plot is generated across the geometric properties _Agent-Goal Distance_ and _Relative Angle_. The individual plots consist of the success predictions of the 10,000 tasks that followed the displayed episode. low relative rotation and distances less than 4 m exhibits a significantly higher success probability. Towards the end of training, the entire task space reaches an estimated success probability close to 100%. We further inspect task distribution from the curriculum in different training stages. Figure 9 displays a set of histograms, which accounts for the number of tasks in terms of one geometric property _Agent-Goal Distance_. In the first 10,000 episodes, a random pattern with respect to the _Agent-Goal Distance_ for the agent _NavACL p.t._ is present. This is reasonable as the agent behaves more randomly at the beginning and mostly ends up with not reaching the target. With merely negative experience, the success prediction network cannot distinguish _easy_ task from _frontier_ task, hence reaching a more or less random pattern. In the intermediate stage, represented by episodes 50,000:60,000, where the agent starts to learn in the initial positions with small relative distance but still fails in large initial distance. This can additionally be verified in Figure 8. In this phase, _easy_ and _frontier_ task corresponds to the regions with close distances. This is referred to as a more concentrated distribution that can be found with the featured goal distances in the range of 1.5 m to 1.5 m. Note that the definition of _easy_ and _frontier_ task also evolves with the training stage. In a later training stage, represented by episodes 150,000:160,000, the success prediction network \(f_{\pi}\) has mostly successful predictions covering all the relative distances in Figure 8. In this case, large initial distances can also be classified as _easy_ task or _frontier_ one, resulting in a random sampling. This tendency is in accordance with the anticipated behavior of _NavACL-Q_. The \(RND\) agent on the other hand, is trained based on randomly sampled tasks only, therefore it shows a uniform distribution across the defined distance domain.