Future-aware Safe Active Learning of Time Varying Systems using Gaussian Processes
Authors: Markus Lange-Hegermann, Christoph Zimmer
TMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Empirical results highlight T-IMSPE s advantages in model quality through synthetic and real-world examples. |
| Researcher Affiliation | Collaboration | Markus Lange-Hegermann EMAIL Department of Electrical Engineering and Institute Industrial IT in IT OWL University of Applied Sciences and Arts Lemgo, Germany Christoph Zimmer EMAIL Bosch Center for Artificial Intelligence Renningen, Germany |
| Pseudocode | Yes | Algorithm 1: Safe Active Learning (SAL) with Gaussian Processes |
| Open Source Code | No | For further results of our experiments resp. further details on the setup of our experiments see Appendix E resp. Appendix F and the attached code. |
| Open Datasets | Yes | We conduct three experiments for safe active learning (Algorithm 1) in time varying systems. Thereby, we demonstrate the superiority of the modeling quality achieved by T-IMSPE over both entropy, which is currently the state of the art (see Appendix D) in active learning, and IMSPE, while keeping the same safety standard. For further results of our experiments resp. further details on the setup of our experiments see Appendix E resp. Appendix F and the attached code. 5.1 Experiment: seasonal change We consider learning a system with strong periodic seasonal changes. The system is given as by rotating the two-dimensional domain in the function from Equation (7) in Appendix F.1 and plotted in Figure 3 with additional plots in the Appendix in Figure 11. 5.2 Experiment: drift We consider learning a system with strong temporal drift. The system is given as by the formula in Equation (8) in Appendix F.1 and plotted in Figure 5 with additional plots in the Appendix in Figure 12 and Figure 13. 5.3 Dynamic real world system: rail pressure This experiment considers the rail pressure example from (Tietze et al., 2014). |
| Dataset Splits | Yes | We start with 8 initial measurements at times 0, . . . , 7 positioned at the inital points of a Sobol sequence in the safe area. Afterwards, 100 further measurements at times 8, . . . , 107 are conducted according to the respective safe active learning criteria T-IMSPE (from Equation 5), entropy, and IMSPE. For the upcoming experiment and the subsequent experiment, we utilize a grid as our test dataset, restricting to grid points where the behavior is currently safe. To obtain test data in the safe area, we constructed a random safe trajectory of length 2024, where the next point is always a random point that turned out to be safe. We choose 256 initial measurements in the known safe domain, while keeping distances between points short enough that the initial measurements are all safe. |
| Hardware Specification | Yes | The first row shows the computation time in seconds on an NVIDIA RTX3080 GPU of all 1000 safe active learning steps. |
| Software Dependencies | No | Our implementation is done in the Py Torch environment (Paszke et al., 2017). For the initial training of the GP hyperparameters, we use the SQP10 implementation from Py Granso (Liang et al., 2022; Curtis et al., 2017). While using GPy Torch (Gardner et al., 2018), we reimplemented the priors to avoid inconsistencies in GPy Torch. |
| Experiment Setup | Yes | All our GPs use the squared exponential covariance function with a separate length scale ℓi as hyperparameter for each input (automatic relevance determinantion). Additionally, we use the signal variance σ2 f and noise variance σ2 n as as additional hyperparameters, as in (Rasmussen & Williams, 2006). The GP has a constant mean function m as hyperparameter. For the initial training of the GP hyperparameters, we use the SQP10 implementation from Py Granso (Liang et al., 2022; Curtis et al., 2017). After each new measurement, we retrain all hyperparameters with 30 steps of ADAM. The optimization for safe active learning is done again using the SQP implementation from Py Granso with 3 random restarts. In case of the first or second unsuccessful optimization, where no point keeping the constraints could be found, we start an additional optimizations with new starting points, such that at most 5 restarts are performed. In the optimizer, all tolerances are set to 10 4 and maximal 200 iterations are allowed. The most important constraints, the safety constraint, is taken msafe(x |x, y) + 2 p ksafe(x |x) < c, where c is the constraint and msafe(x |x, y) resp. p ksafe(x |x) are the mean resp. standard deviation of the posterior GP at x . This corresponds to α = 0.977. We choose the following priors for the experiments. For the seasonal change experiment from Subsection 5.1 and for the drift experiments from Subsection 5.2 the priors are softplus 1(ℓt) N(5, 12) softplus 1(ℓx) N(0, 12) softplus 1(σf) N(1, 12) softplus 1(σn) N( 3, 12) m N(10, 0.012) for softplus(x) = log(1 + exp(x)), temporal length scale ℓt and spatial length scale ℓx. For the rail pressure experiments from Subsection 5.3 the priors are softplus 1(ℓ) N(0.5, 0.12) softplus 1(σf) N(0.5, 0.12) softplus 1(σn) N( 3, 0.12) m N(11.77, 0.012). |