A Dynamic Negative Log-Likelihood Optimization Method for Device Selection in Federated Learning with Over-The-Air Computation

This paper addresses an optimization problem of device selections and aggregation errors in over-the-air computation with federated learning (AirCompFL) systems. To achieve this, we first propose an AirCompFL system model and then formulate the device selections problem as a multi-objective mixed integer programming problem. We then propose a dynamic negative log-likelihood weighted optimization decision (DNLWOD) approach to solve the above problem. The method selects a device based on multiple criteria for enhancing the overall performance, which optimizes the weight of each criterion to balance and minimize aggregation errors automatically and simultaneously. Experimental results show that the DNLWOD method can effectively reduce aggregation errors to enhance the performance of the AirCompFL system, outperforming the existing algorithms in terms of the overall performance, average performance and aggregated error. This work shows that in a wireless edge networking environment with the AirCompFL system, the proposed scheme can provide an effective strategy for selecting devices and optimizing aggregation to increase the communication efficiency and mitigate the aggregation errors.

I. Introduction

The rapid development of future communications and Internet of Things technologies has increased demands for wireless network devices that can perform real-time communication and local computations while meeting communications system high reliability and low latency requirements [1]. To meet this need, a new type of over-the-air computation method has gained widespread attention as a potential solution for enabling efficient and reliable communications between multiple devices in a decentralized manner [2]. As the growth of smart devices in wireless network edges continues, edge computing capabilities are necessary to achieve local training and inferences for reducing data transmission latencies. To promote efficient collaborations among a large number of devices, innovative mechanisms should be developed to improve their communication and computation efficiencies. Over-the-air computation with federated learning (AirCompFL) is an innovative method to support collaborative cooperation among large-scale wireless devices. This strategy allows wireless devices to generate updated models locally and send them directly to the base station (BS). The BS processes the local updates through federated aggregations to generate globally enhanced models, achieving efficient integration of communication and computing and significantly reducing communication latency and power consumption simultaneously [3]. However, the AirCompFL also faces some unique challenges, including those caused by changes in device locations, uncertain factors brought about by unstable channel quality, limited deployment costs, device computing capabilities, and a lack of power resources [4]. Therefore, in the AirCompFL system, device selections and aggregate error communication efficiency optimizations are critical. With the participation of a large number of devices in federated learning, it is challenging to select the optimal devices to obtain better global models.