Reinforcement learning (RL) has achieved remarkable success across various domains; however, its applicability is often hampered by challenges in practicality and interpretability. Many real-world applications, such as in healthcare and business settings, have large and/or continuous state and action spaces and demand personalized solutions. In addition, the interpretability of the model is crucial to decision-makers so as to guide their decision-making process while incorporating their domain knowledge. To bridge this gap, we propose a personalized reinforcement learning framework that integrates personalized information into the state-transition and reward-generating mechanisms. We develop an online RL algorithm for our framework. Specifically, our algorithm learns the embeddings of the personalized state-transition distribution in a Reproduction Kernel Hilbert Space (RKHS) by balancing the exploitation-exploration trade-off. We further provide the regret bound of the algorithm and demonstrate its effectiveness in recommender systems.