Radio network optimization is concerned with the configuration of radio base station parameters in order to achieve the desired level of service quality in addition to many other differentiating technical factors. Mobile network operators have different physical locations, levels of traffic profiles, number of connected devices, and the desired quality of service. All of these conditions make the problem of optimizing the parameters of a radio base station specific to the operator's business goals. The high number of calibration parameters and the complex interaction between them make the system behave as a black-box model for any practical purpose. The computation of relevant operator metrics is often stochastic, and it can take several minutes to compute the effect of changing a single, making it impractical to optimize systems with approaches that require a large number of iterations. Operators want to optimize their already deployed system in online scenarios while minimizing the exposure of the system to a negative set of parameters during the optimization procedure. This paper presents a novel approach to the optimization of a Long Term Evolution (LTE) radio base station in a large search space with an expensive stochastic objective and a limited regret bounds scenario. We show the feasibility of this approach by implementing it in an industrial testing bed radio base station connected to real User Equipment (UE) in collaboration with Ericsson. Two optimization processes in this experimental setup are executed to show the feasibility of the approach in real-world scenarios.