Selecting Informative Data Samples for Model Learning Through Symbolic Regression

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Continual model learning for nonlinear dynamic systems, such as autonomous robots, presents several challenges. First, it tends to be computationally expensive as the amount of data collected by the robot quickly grows in time. Second, the model accuracy is impaired when data from repetitive motions prevail in the training set and outweigh scarcer samples that also capture interesting properties of the system. It is not known in advance which samples will be useful for model learning. Therefore, effective methods need to be employed to select informative training samples from the continuous data stream collected by the robot. Existing literature does not give any guidelines as to which of the available sample-selection methods are suitable for such a task. In this paper, we compare five sample-selection methods, including a novel method using the model prediction error. We integrate these methods into a model learning framework based on symbolic regression, which allows for learning accurate models in the form of analytic equations. Unlike the currently popular data-hungry deep learning methods, symbolic regression is able to build models even from very small training data sets. We demonstrate the approach on two real robots: the TurtleBot mobile robot and the Parrot Bebop drone. The results show that an accurate model can be constructed even from training sets as small as 24 samples. Informed sample-selection techniques based on prediction error and model variance clearly outperform uninformed methods, such as sequential or random selection.