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.