Model-sharing Games: Analyzing Federated Learning Under Voluntary Participation

Federated learning is a setting where agents, each with access to their own data source, combine models learned from local create global model. If agents are drawing different distributions, though, federated might produce biased model that not optimal for agent. This means face fundamental question: should they join the or stay model? In this work, we show how situation can be naturally analyzed through framework of coalitional game theory. Motivated by these considerations, propose following game: there heterogeneous players parameters governing distribution and amounts have noisily drawn distribution. Each player's goal obtain minimal expected mean squared error (MSE) on They choice fitting based solely data, combining those some subset other players. Combining reduces variance component more but increases bias because heterogeneity distributions. derive exact MSE values problems in linear regression estimation. We use analyze resulting hedonic theory; study divide into coalitions, set within coalition jointly constructs single case arbitrarily many either "small" "large" amount constructively always exists stable partition coalitions.