Min-Max Cost Optimization for Efficient Hierarchical Federated Learning in Wireless Edge Networks

Federated learning is a distributed machine learning technology that can protect users’ data privacy, so it has attracted more and more attention in the industry and academia. Nonetheless, most of the existing works focused on the cost optimization of the entire process, while the cost of individual participants cannot be considered. In this article, we explore a min-max cost-optimal problem to guarantee the convergence rate of federated learning in terms of cost in wireless edge networks. In particular, we minimize the cost of the worst-case participant subject to the delay, local CPU-cycle frequency, power allocation, local accuracy, and subcarrier assignment constraints. Considering that the formulated problem is a mixed-integer nonlinear programming problem, we decompose it into several sub-problems to derive its solutions, in which the subcarrier assignment and power allocation are obtained by utilizing the Lagrangian dual decomposition method, the CPU-cycle frequency is obtained by a heuristic algorithm, and the local accuracy is obtained by an iteration algorithm. Simulation results show the convergence of the proposed algorithm and reveal that the proposed scheme can accomplish a tradeoff between the cost and fairness by comparing the proposed scheme with the existing schemes.