Title: Offline Communication Learning with Multi-source Datasets. Abstract: Scalability and partial observability are two major challenges faced by multi-agent reinforcement learning. Recently researchers propose offline MARL algorithms to improve scalability by reducing online exploration cost, while the problem of partial observability is often ignored in the offline MARL setting. Communication is a promising approach to alleviate the miscoordination caused by partially observability, thus in this paper we focus on offline communication learning where agents learn from an fixed dataset. We find out that learning communications in an end-to-end manner from a given offline dateset without communication information is intractable, since the correct communication protocol space is too sparse compared with the exponentially growing joint state-action space when the number of agents increases. Besides, unlike offline policy learning which can be guided by reward signals, offline communication learning is struggling since communication messages implicitly impact the reward. Moreover, in real-world applications, offline MARL datasets are often collected from multi-source, leaving offline MARL communication learning more challenging. Therefore, we present a new benchmark which contains a diverse set of challenging offline MARL communication tasks with single/multi-source datasets, and propose a novel Multi-Head structure for Communication Imitation learning (MHCI) algorithm that automatically adapts to the distribution of the dataset. Empirical result shows the effectiveness of our method on various tasks of the new offline communication learning benchmark.