Mechanism for Collaborative Federated Learning: Pitfalls of Shapley Values

Abstract

This paper investigates the impact of mechanism design on collaborative learning systems enabled by federated learning (FL). We propose a multi-action collaborative federated learning (MCFL) framework, capturing the interplay between agent strategies, platform mechanisms, and FL algorithms--a "three-body problem" in collaborative learning. This work demonstrates how the convergence rate and computational efficiency of FL are endogenously determined by the agent participation equilibrium that is induced by the mechanism. By doing so, we establish a direct link between incentive design in collaborative learning systems and the performance of the underlying optimization algorithms, a connection that has been largely overlooked in the existing literature. Specifically, we characterize the equilibrium of agent participation under two prominent mechanisms: the Shapley Value (SV) and Marginal Contribution (MC) mechanisms. Although SV is fair in surplus allocation and budget balanced, it has a vital pitfall: agents are incentivized to split their data across newly created fake identities. This is critical especially in the MCFL setting as it leads to slow convergence of FL optimization, which increases the number of required synchronization/communication rounds even when the per-round cost is fixed. In contrast, while MC is not budget-balanced, it is robust to such strategic manipulation and is able to induce an equilibrium that maximizes the MCFL system efficiency. Overall, our study lays a foundation for jointly designing incentives and algorithms in MCFL systems. We provide insights on pitfalls of SV: it induces a system equilibrium that leads to tremendous training cost and slower convergence, ultimately undermining the effectiveness of collaborative learning.