Abstract: Massive amounts of data are naturally dispersed over different clients in many real-world applications, collaborative learning has been a promising paradigm that allows to learn models through collaboration among the clients. However, leveraging these dispersed data to learn good models is still challenging since data over different clients are heterogeneous. Previous works mainly focus on learning the centralized model for all clients or learning a personalized model for each client. When there are numerous clients, the centralized model performs badly on some clients, while learning a personalized model for each client costs unaffordable computational resources. In this paper, we propose the collaborative learning method to detect collaboration partners and adaptively learn $K$ models for numerous heterogeneous clients. We theoretically prove that the model learned for each client is a good approximation of its personalized model. Experimental results on real-world datasets verify the effectiveness of our method.