Abstract. In this paper, the problem of safe exploration in the active learning context is considered. Safe exploration is especially important for data sampling from technical and industrial systems, e.g. combustion engines and gas turbines, where critical and unsafe measurements need to be avoided. The objective is to learn data-based regression models from such technical systems using a limited budget of measured, i.e. labelled, points while ensuring that critical regions of the considered systems are avoided during measurements. We propose an approach for learning such models and exploring new data regions based on Gaussian processes (GP's). In particular, we employ a problem specific GP classifier to identify safe and unsafe regions, while using a differential entropy criterion for exploring relevant data regions. A theoretical analysis is shown for the proposed algorithm, where we provide an upper bound for the probability of failure. To demonstrate the efficiency and robustness of our safe exploration scheme in the active learning setting, we test the approach on a policy exploration task for the inverse pendulum hold up problem.
When modeling technical systems as black-box models, it is crucial to obtain as much and as informative measurement data as possible in the shortest time while employing safety constraints. Methods for an optimized online generation of measurement data are discussed in the field of Active Learning. Safe Active Learning combines the optimization of the query strategy regarding model quality with an exploration scheme in order to maintain userdefined safety constraints. In this paper, the authors apply an approach for Safe Active Learning based on Gaussian process models (GP models) to the high pressure fuel supply system of a gasoline engine. For this purpose, several enhancements of the algorithm are necessary. An online optimization of the GP models' hyperparameters is implemented, where special measures are taken to avoid a safety-relevant overestimation. A proper risk function is chosen and the trajectory to the sample points is taken into account regarding the estimation of the samples feasibility. The algorithm is evaluated in simulation and at a test vehicle.
Sparse Gaussian process (GP) models provide an efficient way to perform regression on large data sets. The key idea is to select a representative subset of the available training data, which induces the sparse GP model approximation. In the past, a variety of selection criteria for GP approximation have been proposed, but they either lack accuracy or suffer from high computational costs. In this paper, we introduce a novel and straightforward criterion for successive selection of training points used for GP model approximation. The proposed algorithm allows a fast and efficient selection of training points, while being competitive in learning performance. As evaluation, we employ our approach in learning inverse dynamics models for robot control using very large data sets (e.g. 500.000 samples). It is demonstrated in experiments that our approximated GP model is sufficiently fast for real-time prediction in robot control. Comparisons with other state-of-the-art approximation techniques show that our proposed approach is significantly faster, while being competitive to generalization accuracy.
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