This paper is about a real-time model predictive control (MPC) algorithm for a particular class of model based controllers, whose objective consists of a nominal tracking objective and an additional learning objective. Here, the construction of the learning term is based on an economic optimal experiment design criterion. It is added to the MPC objective in order to excite the system on purpose thereby improving the accuracy of the state and parameter estimates in the presence of incomplete or noise affected measurements. The focus of this paper is on so-called self-reflective model predictive control schemes, which have the property that the additional learning term can be interpreted as the expected loss of optimality of the controller in the presence of random measurement errors. The main contribution is a formulation tailored algorithm, which exploits the particular structure of self-reflective MPC problems in order to speed-up the online computation. It is shown that the proposed algorithm can solve the self-reflective optimization problems with reasonable additional computational effort and in real-time. (C) 2017 Elsevier Ltd. All rights reserved.