This contribution presents a meta-modeling framework that employs artificial intelligence to design a neural network that replicates the path-dependent constitutive responses of composite materials sampled by a numerical testing procedure of Representative Volume Elements (RVE). A Deep Reinforcement Learning (DRL) combinatorics game is invented to automatically search for the optimal set of hyper-parameters from a decision tree. Besides the typical hyper-parameters for ANN training, such as the network topology, the size and composition of the considered training data are incorporated as additional hyper-parameters to help investigate the amount of data necessary for training and validation. The proposed meta modeling framework is able to identify hyper-parameter configurations with a weighted trade-off between prediction accuracy and computational cost. The capabilities and limitations of the introduced framework are shown and discussed via several numerical examples. Moreover, the possibility of transferring the gained knowledge of hyper-parameters among different RVE is explored in numerical experiments.