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Conversational Recommender Systems (CRSs) are intelligent E-commerce applications that engage online users in an interactive conversation, until their interaction goal is achieved. To this end, traditional CRSs employ a recommendation strategy that is pre-determined by the system designers and followed rigidly during the recommendation session. In a previous paper, we have introduced a new type of a CRS that uses Reinforcement Learning (RL) techniques in order to autonomously learn an optimal recommendation strategy. This strategy is optimal in a context defined by RL, and is adapted to the interacting user population. We have validated our approach in both an offline and online context. Notwithstanding our successful results, we argue that the ideal goal of an online user-adaptation process is to adapt separately to the individual behaviors of the users. In this paper, we address this issue. Through offline simulations, we show that our approach is able to learn intelligent optimal strategies that are separately adapted to a specific behavior of the individual (simulated) users. In order to test the robustness of the optimal behavior, we repeated the experiments with different RL configurations, and we achieved similar results.