Coalitional Game Theoretic Federated Learning

This study approaches federated learning (FL) from the viewpoint of coalitional games with coalition structure generation (CSG). In conventional FL, even if each client has data from a different distribution, they still learn a single global model. However, the performance of each local model can degrade. To address such issues, we propose an algorithm in which clients form coalitions and the clients in the same coalition jointly train a specialized model for the coalition, namely a coalition model. We formulate the algorithm as a graphical coalition game given by a weighted undirected graph in which a node indicates a client and the weight of an edge indicates the synergy between two connected clients. Formulating FL as a CSG problem enables us to generate an optimal CS that maximizes the sum of synergies. We first define two types of synergy, i.e., that based on the average improvement in classification accuracy of two agents as they join the same coalition and that based on the cosine similarity between the gradients of the loss functions, which is intended to exclude adversaries having adversarial data from a set of nonadversaries. We conduct experiments to evaluate our algorithm, and the results indicate that it outperforms current algorithms.