Alliance Makes Difference? Maximizing Social Welfare in Cross-Silo Federated Learning

As one of the typical settings of Federated Learning (FL), cross-silo FL allows organizations to jointly train an optimal Machine Learning (ML) model. In this case, some organizations may try to obtain the global model without contributing their local training power, lowering the social welfare. In this paper, we model the interactions among organizations in cross-silo FL as a public goods game and theoretically prove that there exists a social dilemma where the maximum social welfare is not achieved in Nash equilibrium. To overcome this dilemma, we employ the Multi-player Multi-action Zero-Determinant (MMZD) strategy to maximize the social welfare. With the help of the MMZD, an individual organization can unilaterally control the social welfare without extra cost. Since the MMZD strategy can be adopted by all organizations, we further study the case of multiple organizations jointly adopting the MMZD strategy to form an MMZD Alliance (MMZDA). We prove that the MMZDA strategy can strengthen the control of the maximum social welfare. Experimental results validate that the MMZD strategy is effective in obtaining the maximum social welfare and the MMZDA can achieve a larger maximum value.