Personalized federated learning enables every edge device or group of edge devices within the distributed network to learn a device-or cluster-specific model tailored to their local needs. Data scarcity, however, makes it difficult to learn such individual models, resulting in performance degradation. Since the device-or cluster-specific tasks are distinct but often related, leveraging these similarities through inter-cluster learning alleviates data shortage and enhances learning performance. Although inter-cluster learning can boost performance, uncontrolled intercluster learning may lead to performance degradation due to over-or under-usage of local similarity enforcement. In light of this issue, an intelligent mechanism that performs inter-cluster learning based on device-specific needs is required. To this end, this paper proposes adopting reinforcement learning principles to control device-specific inter-cluster learning in real-time. We propose networked personalized federated learning using reinforcement learning (NPFed-RL) as a general framework and then demonstrate its feasibility by applying it to the ridge regression problem. We conduct numerical experiments to compare the proposed method with the state-of-the-art. The proposed method successfully controls device-specific parameters and offers better learning performance than existing solutions.