Joint Optimization of Bandwidth Allocation and Gradient Quantization for Federated Edge Learning

Abstract

Federated Edge Learning (FEEL) is becoming a popular distributed privacy-preserving machine learning (ML) framework where multiple edge devices collaboratively train an ML model with the help of an edge server. However, FEEL usually suffers from a communication bottleneck due to the limited sharing wireless spectrum as well as the large size of training parameters. In this paper, we consider gradient quantization to reduce the communication traffic and aim at minimizing the total training latency. Since the per-round latency is determined by both the bandwidth allocation scheme and gradient quantization scheme (i.e., the quantization levels of edge devices), while the number of training rounds is affected by the latter, we propose a joint optimization of bandwidth allocation and gradient quantization. Based on the analysis of total training latency, we first formulate the joint optimization problem as nonlinear integer programming. To solve this problem, we then consider a variation of this problem where the per-round latency is fixed. Although this variation is proved to be NP-hard, we show that it can be transformed into a multiple-choice knapsack problem which can be solved efficiently by a pseudopolynomial time algorithm based on dynamic programming. We further propose a ternary search based algorithm to find a near-optimal per-round latency, so that the two algorithms together can yield a near-optimal solution to the joint optimization problem. The effectiveness of our proposed approach is validated through simulation experiments.