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Reinforcement Learning algorithms aim to learn optimal control strategies through iterative interactions with an environment. A critical element in this process is the experience replay buffer, which stores past experiences, allowing the algorithm to learn from a diverse range of interactions rather than just the most recent ones. This buffer is especially essential in dynamic environments with limited experiences. However, efficiently selecting high-value experiences to accelerate training remains a challenge. Drawing inspiration from the role of reward prediction errors (RPEs) in biological systems, where they are essential for adaptive behaviour and learning, we introduce Reward Predictive Error Prioritised Experience Replay (RPE-PER). This novel approach prioritises experiences in the buffer based on RPEs. Our method employs a critic network, EMCN, that predicts rewards in addition to the Q-values produced by standard critic networks. The discrepancy between these predicted and actual rewards is computed as RPE and utilised as a signal for experience prioritisation. Experimental evaluations across various continuous control tasks demonstrate RPE-PER's effectiveness in enhancing the learning speed and performance of off-policy actor-critic algorithms compared to baseline approaches., Comment: This paper was accepted for presentation at the 2024 Australasian Conference on Robotics and Automation (ACRA 2024). It consists of 10 pages, including four figures and two tables