Federated Learning (FL) is a promising framework for distributed learning when data is private and sensitive. However, the state-of-the-art solutions in this framework are not optimal when data is heterogeneous and non-IID. We propose a practical and robust approach to personalization in FL that adjusts to heterogeneous and non-IID data by balancing exploration and exploitation of several global models. To achieve our aim of personalization, we use a Mixture of Experts (MoE) that learns to group clients that are similar to each other, while using the global models more efficiently. We show that our approach achieves an accuracy up to 29.78% better than the state-of-the-art and up to 4.38% better compared to a local model in a pathological non-IID setting, even though we tune our approach in the IID setting.