Plasma medicine has emerged as a promising approach for treatment of biofilm-related and virus infections, assistance in cancer treatment, and treatment of wounds and skin diseases. Despite advances in learning-based and predictive control of plasma medical devices, there remain major challenges towards personalized and point-of-care plasma medicine. In particular, an important challenge arises from the need to adapt control policies after each treatment using (often limited) observations of therapeutic effects that can only be measured between treatments. Control policy adaptation is necessary to account for variable characteristics of plasma and target surfaces across different subjects and treatment scenarios, thus personalizing the plasma treatment to enhance its efficacy. To this end, this paper presents a data-efficient, "globally" optimal strategy to adapt deep learning-based controllers that can be readily embedded on resource-limited hardware for portable medical devices. The proposed strategy employs multi-objective Bayesian optimization to adapt parameters of a deep neural network (DNN)-based control law using observations of closed-loop performance measures. The proposed strategy for adaptive DNN-based control is demonstrated experimentally on a cold atmospheric plasma jet with prototypical applications in plasma medicine.