## 4 Results
### Ablation Studies
#### 4.3.1 Ablation Studies: Effects of Automatic Curriculum Learning  
To investigate the effects of our automatic curriculum approach _NavACL-Q_, we compare it with the variant _RND_, where _RND_ has the same setting as _NavACL-Q p.t._ except that it samples the initial state randomly from the defined boundary. It is first to be noted that _RND_ is already an approach encouraging the exploration and alleviates the task difficulty compared to a fixed distant initial position from the target [15]. If a better training performance can be witnessed from _NavACL-Q_, then the effectiveness of our automatic curriculum learning approach can be verified. We demonstrate the comparison both in training and testing performance. Figure 5 reveals that in the training phase the _RND_ method imposes the highest training variance. One of the three trials meets the 90% threshold in the _RND_ case, though the other two trials have not exceeded 40% performance, resulting in an average final performance of approximately 50%. In contrast, the variance of _NavACL-Q e.t.e._ remains small, i.e., more robust. This can also be validated from the variant _NavACL-Q e.t.e._, which also incorporates the component of _NavACL-Q_. Moreover, the _NavACL-Q p.t._ exhibits a consistently faster improvement at the initial stage of training. With 1\(M\) steps, _RND_ just starts to show a sign of improving in terms of success rate whereas _NavACL-Q p.t._ has already reached the average success rate of 30% in Figure 5b. From these observations, it can be concluded that _NavACL-Q_ indeed facilitates the training in terms of both final converged value and rate of convergence. We further present a summary statistics for a comparison on the testing performance in Table 3, _NavACL-Q p.t._ achieves approximately 90% success rate in navigating underneath the dolly among four out of five intrapolated initial orientations, outperforming _RND_ by at least 30%. Moreover, _NavACL-Q p.t._ reveals the best performance averaged over all orientations, surpassing _RND_ by 11% for all tested orientations including the extrapolated ones. Overall speaking, _NavACL-Q p.t._ converges to a better policy than _RND_ in the testing case. Moreover, both _RND_ and _NavACL-Q p.t._ suggest general decreasing tendencies of success rates with increasing relative initial orientations, which is reasonable as the effect of partial observability aggregates with higher relative orientations. Figure 7: Color-coded illustration on the grid-based testing result of one fully trained _NaxACL-Q_ agent. The average performance for each position on the grid is represented by a colorized circle, where yellow color indicates a high success rate and blue color indicates near-zero success probability. (**a**) The testing result of _NaxACL-Q_ _p.t._ (**b**) The testing result of _RND_ (**c**) The testing result of _NaxACL-Q_ _e.t._ A further summary of the statistics is available in Table 3.  
We take a closer look at whether the success prediction network \(f_{\pi}\) in _NavACL-Q p.t._ shows meaningful predicted success probability and how it evolves with the training stages. To examine this effect, the outputs of \(f_{\pi}\) are evaluated across different stages of training from one of the three runs. Figure 8 illustrates predicted task success rate in the defined regions with respect to two geometric properties, initial robot orientation and the Euclidean distance between initial robot pose and target dolly. These two properties give a straightforward view on the task difficulty. For instance, a small initial rotation angle with close distance is regarded as optimistic initial position. It is hypothesized that a well-learned \(f_{\pi}\) should show a increasing tendency on success probability as the training progresses. Besides, the prediction network should also distinguish favorable initial poses from unfavorable ones. As can be observed from Figure 8, at the initial training stage, e.g., episode 0, the agent behaves totally in a random fashion and a general low predicted success value can be expected.