Multiplayer Federated Learning: Reaching Equilibrium with Less Communication

Traditional Federated Learning (FL) approaches assume collaborative clients with aligned objectives working toward a shared global model. However, in many real-world scenarios, clients act as rational players with individual objectives and strategic behavior, a concept that existing FL frameworks are not equipped to adequately address. To bridge this gap, we introduce Multiplayer Federated Learning (MpFL), a novel framework that models the clients in the FL environment as players in a game-theoretic context, aiming to reach an equilibrium. In this scenario, each player tries to optimize their own utility function, which may not align with the collective goal. Within MpFL, we propose Per-Player Local Stochastic Gradient Descent (PEARL-SGD), an algorithm in which each player/client performs local updates independently and periodically communicates with other players. We theoretically analyze PEARL-SGD and prove that it reaches a neighborhood of equilibrium with less communication in the stochastic setting compared to its nonlocal counterpart. Finally, we verify our theory through numerical experiments.

• Constant step-size: We show that under the same assumptions as in the deterministic case, PEARL-SGD converges linearly to a neighborhood of equilibrium (see Theorem 3.4). In Corollary 3.5, we show that with appropriate step-size depending on the total number of local SGD iterations T , PEARL-SGD achieves Õ(1/T ) convergence rate with improved communication complexity when T is sufficiently large. * Decreasing step-size rule: We prove that PEARL-SGD converges to an exact equilibrium (without neighborhood of convergence) with sublinear convergence (see Theorem 3.6). In this scenario, the asymptotic rate and communication complexity are essentially the same as in Corollary 3.5, but this result does not require the step-sizes to depend on T .

• Numerical Evaluation: We provide numerical experiments verifying our theoretical results and show the benefits in terms of communications of PEARL-SGD over its non-local counterpart in the MpFL settings.