Twin Sorting Dynamic Programming Assisted User Association and Wireless Bandwidth Allocation for Hierarchical Federated Learning

In this paper, we study user association and wireless bandwidth allocation for a hierarchical federated learning system that consists of mobile users, edge servers, and a cloud server. To minimize the length of a global round in hierarchical federated learning with equal bandwidth allocation, we formulate a combinatorial optimization problem. We design the twin sorting dynamic programming (TSDP) algorithm that obtains a globally optimal solution in polynomial time when there are two edge servers. In addition, we put forward the TSDP-assisted algorithm for user association when there are three or more edge servers. Furthermore, given a user association matrix, we formulate and solve a convex optimization problem for optimal wireless bandwidth allocation. Simulation results show that the proposed approach outperforms a number of alternative schemes.