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Shapley Value is commonly adopted to measure and incentivize clientparticipation in federated learning. In this paper, we show -- theoreticallyand through simulations -- that Shapley Value underestimates the contributionof a common type of client: the Maverick. Mavericks are clients that differboth in data distribution and data quantity and can be the sole owners ofcertain types of data. Selecting the right clients at the right moment isimportant for federated learning to reduce convergence times and improveaccuracy. We propose FedEMD, an adaptive client selection strategy based on theWasserstein distance between the local and global data distributions. As FedEMDadapts the selection probability such that Mavericks are preferably selectedwhen the model benefits from improvement on rare classes, it consistentlyensures the fast convergence in the presence of different types of Mavericks.Compared to existing strategies, including Shapley Value-based ones, FedEMDimproves the convergence of neural network classifiers by at least 26.9% forFedAvg aggregation compared with the state of the art.

Is Shapley Value fair? Improving Client Selection for Mavericks in Federated Learning