t User satisfaction is often considered as the objective that should be achieved by spoken dialogue systems. This is why, the reward function of Spoken Dialogue Systems (SDS) trained by Reinforcement Learning (RL) is often designed to reflect user satisfaction. To do so, the state space representation should be based on features capturing user satisfaction characteristics such as the mean speech recognition confidence score for instance. On the other hand, for deployment in industrial systems, there is a need for state representations that are understandable by system engineers. In this paper, we propose to represent the state space using a Genetic Sparse Distributed Memory. This is a state aggregation method computing state prototypes which are selected so as to lead to the best linear representation of the value function in RL. To do so, previous work on Genetic Sparse Distributed Memory for classification is adapted to the Reinforcement Learning task and a new way of building the prototypes is proposed. The approach is tested on a corpus of dialogues collected with an appointment scheduling system. The results are compared to a grid-based linear parametrisation. It is shown that learning is accelerated and made more memory efficient. It is also shown that the framework is calable in that it is possible to include many dialogue features in the representation, interpret the resulting policy and identify the most important dialogue features.