Joint Edge Aggregation and Association for Cost-Efficient Multi-Cell Federated Learning

Federated learning (FL) has been proposed as a promising distributed learning paradigm to realize edge artificial intelligence (AI) without revealing the raw data. Nevertheless, it would incur inevitable costs in terms of training latency and energy consumption, due to periodical communication between user equipments (UEs) and the geographically remote central parameter server. Thus motivated, we study the joint edge aggregation and association problem to minimize the total cost, where the model aggregation over multiple cells just happens at the network edge. After proving its hardness with complex coupled variables, we transform it into a set function optimization problem and prove the objective function is neither submodular nor supermodular, which further complicates the problem. To tackle this difficulty, we first split it into multiple edge association subproblems, where the optimal solution to the computation resource allocation can be efficiently obtained in the closed form. We then construct a substitute function with the supermodularity and provable upper bound. On this basis, we reformulate an equivalent set function minimization problem under a matroid base constraint. We then propose an approximation algorithm to the original problem based on the two-stage search strategy with theoretical performance guarantee. Both extensive simulations and field experiments are conducted to validate the effectiveness of our proposed solution.