- Abstract: Supervised machine learning is often applied to identify system dynamics where first principle methods fail. When combining learning with control methods, probabilistic regression is typically applied to increase robustness against learning errors and analyze the stability of the closed-loop system. Although this approach allows to formulate performance guarantees for many control techniques, the obtained bounds are usually conservative, and cannot be employed for efficient control parameter tuning. Therefore, we reformulate the parameter tuning problem using robust optimization with performance constraints based on Lyapunov theory. By relaxing the problem through scenario optimization we derive a provably optimal method for control parameter tuning. We demonstrate its flexibility and efficiency on parameter tuning problems for a feedback linearizing and a computed torque controller.