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Neutron spin echo (NSE) spectroscopy is a dynamical neutron scattering technique in high demand worldwide. Experiments are long, typically ranging from hours to days, such that small improvements in measurement efficiency translate into substantial reductions in experimental costs. Active learning (AL), in which new measurement conditions are chosen based on the experimental data collected so far, has previously been shown to significantly improve data collection rates for one-dimensional neutron reflectometry patterns. These AL algorithms used Bayesian inference to evaluate the uncertainty in a model of the neutron reflectometry pattern, while the acquisition function selected new measurement conditions that were expected to reduce uncertainty in specific model parameters of interest. Similarly, the NSE response function is a highly nonlinear, one-dimensional damped sinusoid, with the added benefit of an analytical form. Here, we compare the performance of AL algorithms, informed by Bayesian inference and driven by different acquisition functions, for measurement of the NSE response function. We find that general acquisition functions designed to most efficiently reduce the global uncertainty in the model function perform well in large search spaces, while AL algorithms based on acquisition functions that highlight specific parameters significantly outperform the general models at that task. For the NSE function, the AL algorithm is robust even against vanishingly small signals. Finally, fast convergence of the global function does not necessarily imply fast convergence of any individual parameter describing it; thus, if possible, it is important to identify and optimize the specific parameters of interest.