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Next Point-of-Interest (POI) recommendation has become an indispensable functionality in Location-based Social Networks (LBSNs) due to its effectiveness in helping people decide the next POI to visit. However, accurate recommendation requires a vast amount of historical check-in data, thus threatening user privacy as the location-sensitive data needs to be handled by cloud servers. Although there have been several on-device frameworks for privacy-preserving POI recommendations, they are still resource-intensive when it comes to storage and computation, and show limited robustness to the high sparsity of user-POI interactions. On this basis, we propose a novel decentralized collaborative learning framework for POI recommendation (DCLR), which allows users to train their personalized models locally in a collaborative manner. DCLR significantly reduces the local models' dependence on the cloud for training, and can be used to expand arbitrary centralized recommendation models. To counteract the sparsity of on-device user data when learning each local model, we design two self-supervision signals to pretrain the POI representations on the server with geographical and categorical correlations of POIs. To facilitate collaborative learning, we innovatively propose to incorporate knowledge from either geographically or semantically similar users into each local model with attentive aggregation and mutual information maximization. The collaborative learning process makes use of communications between devices while requiring only minor engagement from the central server for identifying user groups, and is compatible with common privacy preservation mechanisms like differential privacy. We evaluate DCLR with two real-world datasets, where the results show that DCLR outperforms state-of-the-art on-device frameworks and yields competitive results compared with centralized counterparts.