On the Accuracy-Energy Tradeoff for Hierarchical Federated Learning via Satisfaction Equilibrium

Hierarchical Federated Learning (HFL) has recently emerged as a promising method to overcome the limitations of conventional Federated Learning (FL) in terms of communication inability of the end users with the cloud and increased backhaul network traffic when considering implementations over wireless networks. Nevertheless, to reap the benefits of HFL, proper user association with the different edge servers and wireless resource allocation is required. Unlike existing works - that in their majority treat unilaterally a single objective using centralized optimization techniques - in this paper, we particularly aim to explore the tradeoff induced between the users' local model training accuracy and personal energy consumption in a distributed manner. The joint problem of user-to-edge-server association and uplink power allocation for transmitting the users' local model parameters to the edge is formulated and solved as a game in satisfaction form. Each user autonomously seeks to achieve a target accuracy-energy ratio by selecting their edge association and uplink transmission power level, while their cumulative decisions result in a desired Satisfaction Equilibrium (SE) point. Specifically, to determine the respective SE of the formulated game, a Reinforcement Learning (RL) algorithm is utilized. Numerical results obtained via modeling and simulation demonstrate the operational and performance characteristics of the proposed framework in terms of achieving the users' personally desired tradeoff value.