Title: Coalitional Personalized Federated Learning: A Hedonic Game Perspective
Primary area: learning theory
Keywords: Federated Learning, Hedonic Game, Coalition Formation

Abstract: This paper presents a novel coalitional personalized federated learning (CPFL) framework through a hedonic game model, enabling self-interested agents to form coalitions for learning. Departing from previous approaches limited to homogeneous priors over one-dimensional parameters, we address the more general case of heterogeneous priors. We characterize both socially optimal and stable coalition structures under two typical agent configurations: the atomic regime with equal sample size and non-atomic regime. We show that the optimization problems can be reduced to well-studied formulations, which are solvable by existing algorithms. Our key algorithmic contributions include BIdirectional-SCAN (BISCAN) and SPREAD, two algorithms for coalition structure formation satisfying both in-coalition stability and individual stability in each agent configuration. Furthermore, we discuss the optimality problem within high-dimensional parameter spaces, extending the one-dimensional theoretical results.