Price-Discrimination Game for Distributed Resource Management in Federated Learning

In federated learning (FL) systems, the parameter server (PS) and clients form a monopolistic market, where the number of PS is far less than the number of clients. To improve the performance of FL and reduce the cost to incentive clients, this letter suggests distinguishing the pricing of FL services provided by different clients, rather than applying the same pricing to them. The price is differentiated based on the performance improvements brought to FL by clients and their heterogeneity in computing and communication capabilities. To this end, a price-discrimination game (PDG) is formulated to comprehensively address the distributed resource management problems in FL, including multi-objective trade-off, client selection, and incentive mechanism. As the PDG includes a mixed-integer nonlinear programming problem, a distributed semi-heuristic algorithm with low computational complexity and low communication overhead is designed to solve the Nash equilibrium (NE) of the PDG. The simulation result verifies that the NE achieves a good tradeoff between the training loss, training time, and the cost of motivating clients to participate in FL.