Modern large-scale computing deployments consist of complex applications running over machine clusters. An important issue in these is the offering of elasticity, i.e., the dynamic allocation of resources to applications to meet fluctuating workload demands. Threshold based approaches are typically employed, yet they are difficult to configure and optimize. Approaches based on reinforcement learning have been proposed, but they require a large number of states in order to model complex application behavior. Methods that adaptively partition the state space have been proposed, but their partitioning criteria and strategies are sub-optimal. In this work we present MDP_DT, a novel full-model based reinforcement learning algorithm for elastic resource management that employs adaptive state space partitioning. We propose two novel statistical criteria and three strategies and we experimentally prove that they correctly decide both where and when to partition, outperforming existing approaches. We experimentally evaluate MDP_DT in a real large scale cluster over variable not-encountered workloads and we show that it takes more informed decisions compared to static and model-free approaches, while requiring a minimal amount of training data.