## 5 Results
### Curriculum Learning by SGIM-PB  
Given the properties of imitation and procedures that we outlined, is SGIM-PB capable of choosing the right strategy for each task to build a curriculum starting from simple tasks before complex tasks? Figure 14 shows that SGIM-PB uses more procedural exploration and imitation than action exploration or imitation for \(\Omega_{3}\) and \(\Omega_{4}\), compared to the more simple tasks. A coupling appears between simple tasks and action space exploration on the one hand, and complex tasks and procedure exploration on the other hand. Moreover, for imitation, **SGIM-PB was overall able to correctly identify the most adapted teacher to each outcome space**. Their only suboptimal choice is to use the procedural teacher built for \(\Omega_{4}\) to explore \(\Omega_{3}\). This mistake can be explained as both outcome spaces have the same task decomposition (see Figure 2). Likewise, for the simulation setup, in Figure 11, the histogram of explored task-strategy combinations confirms that the learner uses mostly autonomous exploration strategies. It uses mostly action exploration for the simplest outcome spaces \((\Omega_{0},\Omega_{1},\Omega_{2})\), and procedure exploration for the most complex outcomes \((\Omega_{3},\Omega_{4})\). This shows the complementarity of action and procedures for exploration in an environment with a hierarchical set of outcome spaces. We can see for each task subspace, the proportion of imitation used. While for \(\Omega_{0}\), SGIM-PB uses the strategy AutonomousActions five times more than ActionTeacher0, the proportion of imitation increases for the complex tasks. Imitation seems to be required more for complex tasks. For the simplest outcome spaces \((\Omega_{0},\Omega_{1},\Omega_{2})\), it uses mostly action exploration and procedure exploration for the most complex ones \((\Omega_{3},\Omega_{4})\). From Figure 11, we can also confirm that for each task, the teacher most requested is specialised in the goal task, the only exceptions are ProceduralTeacher3 and ProceduralTeacher4 who are specialised in different complex tasks but that use the same subtask decomposition, thus demonstrations of ProceduralTeacher3 has effects on \(\Omega_{4}\) and vice versa. The choices shown in the histogram show that SGIM-PB has spotted the teacher's domain of expertise. Let us analyse the evolution of the time each outcome space (Figure 9) and strategy (Figure 10) is chosen during the learning process of SGIM-PB on the simulated setup. In Figure 9, its self-assigned curriculum starts by exploring the most simple task \(\Omega_{0}\) until 1000 iterations. In Figure 10, we see that this period corresponds mainly to the use of the strategy Autonomous policies, relying on itself to acquire its body schema. Then  
Figure 14: Choices of strategy and goal outcome for the SGIM-PB learner during the learning process on the physical setup. it gradually switches to working on the most complex outcome space \(\Omega_{3}\) (the highest dimension) and marginally more on \(\Omega_{4}\) while preferring autonomous procedures and marginally the teachers for \(\Omega_{3}\) and \(\Omega_{4}\). In contrast, the strategy ActionTeacher0 decreases, SGIM-PB does not use action imitation any more. **SGIM-PB switches from imitation of action primitives to procedures, and most of all it turns to the strategies autonomous policies and autonomous procedures**. For the physical setup, the evolution of outcome spaces (Figure 15) and strategies (Figure 16) chosen are more difficult to analyse. However, they show the same trend from iterations 0 to 10,000: the easy outcome spaces \(\Omega_{0},\Omega_{1},\Omega_{2}\) are more explored in the beginning before being neglected after 1000 iterations to explore the most complex outcome spaces \(\Omega_{3},\Omega_{5}\). Imitation is mostly used in the beginning of the learning process, whereas later in the curriculum, autonomous exploration is preferred. The autonomous exploration of actions strategy was also less used.