Model-based evolutionary algorithms (MBEAs) are praised for their broad applicability to black-box optimization problems. In practical applications however, they are mostly used to repeatedly optimize different instances of a single problem class, a setting in which specialized algorithms generally perform better. In this paper, we introduce the concept of a new type of MBEA that can automatically specialize its behavior to a given problem class using tabula rasa self-learning. For this, reinforcement learning (RL) is a naturally fitting paradigm. A proof-of-principle framework, called SL-ENDA, based on estimation of normal distribution algorithms in combination with reinforcement learning is defined. SL-ENDA uses an RL-agent to decide upon the next population mean while approaching the rest of the algorithm as the environment. A comparison of SL-ENDA to AMaLGaM and CMA-ES on unimodal noiseless functions shows mostly comparable performance and scalability to the broadly used and carefully manually crafted algorithms. This result, in combination with the inherent potential of self-learning model-based evolutionary algorithms with regard to specialization, opens the door to a new research direction with great potential impact on the field of model-based evolutionary algorithms.