The potential of spanwise traveling transversal sinusoidal surface waves as an active drag reduction strategy for turbulent boundary layer flows is investigated using wall-resolved large-eddy simulations (LES). LES predictions are performed for Mach numbers \(\textrm{M} = 0.2\) and 0.7 for a fixed momentum-thickness-based Reynolds number of \(\textrm{Re}_{\theta }=1000\) to cover various flow conditions and to extend a previous data set beyond Mach numbers of \(\textrm{M} = 0.1\) . These initial LES data points are planned according to a near-random space-filling sampling method, i.e., Latin hypercube sampling (LHS), within the space of promising actuation parameters. The main goal of surrogate-based optimization is to choose the actuation parameters such that the objective of drag reduction for given flow conditions is maximized by exploiting and exploring the surrogate model, which is fitted to the data and enriched with prior knowledge. Two surrogate-based optimization (SO) strategies using support vector regression (SVR) and Gaussian process regression (GPR) are investigated. To compare both strategies, the simulation data for \(\textrm{M} = 0.1\) are used to model the dependence of the objective drag reduction on the actuation parameters. A previous purely exploitative approach of SVR-based ridgeline optimization (RO) for \(\textrm{M} = 0.1\) is extended to GPR-based Bayesian optimization (BO) to further automate and efficiently guide the CFD-based optimization of the actuation parameters.