Feature Space Transformation using Equation Discovery

In Machine Learning, the success and performance of learning often critically depends on the feature space provided. For instance, when learning a classifier f1, . . . , fn → c that maps features f1, . . . , fn to classes c, appropriate encodings of f1, . . . , fn are often as important as the choice of learning algorithm itself. This is particularly true for robot learning, where feature spaces are typically high dimensional and features are continuous. Consider an example from a robotic navigation, depicted in Figure 1. In [1], the robot learns to predict navigation execution duration given the current and goal pose, from observed experience. By exploiting translational and rotational invariances, the original 6-dimensional state space can be reduced to 3 dimensions. The benefit is that fewer examples are needed to learn an accurate prediction model.