1 Federated Learning via Unmanned Aerial Vehicle

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Federated Learning via Unmanned Aerial

Vehicle

Min Fu, Member, IEEE, Yuanming Shi, Senior Member, IEEE,

and Yong Zhou, Member, IEEE

Abstract

To enable communication-efﬁcient federated learning (FL), this paper studies an unmanned aerial

vehicle (UAV)-enabled FL system, where the UAV coordinates distributed ground devices for a shared

model training. Speciﬁcally, by exploiting the UAV’s high altitude and mobility, the UAV can proac-

tively establish short-distance line-of-sight links with devices and prevent any device from being a

communication straggler. Thus, the model aggregation process can be accelerated while the cumulative

model loss caused by device scheduling can be reduced, resulting in a decreased completion time.

We ﬁrst present the convergence analysis of FL without the assumption of convexity, demonstrating

the effect of device scheduling on the global gradients. Based on the derived convergence bound, we

further formulate the completion time minimization problem by jointly optimizing device scheduling,

UAV trajectory, and time allocation. This problem explicitly incorporates the devices’ energy budgets,

dynamic channel conditions, and convergence accuracy of FL constraints. Despite the non-convexity

of the formulated problem, we exploit its structure to decompose it into two sub-problems and further

derive the optimal solutions via the Lagrange dual ascent method. Simulation results show that the

proposed design signiﬁcantly improves the tradeoff between completion time and prediction accuracy

in practical FL settings compared to existing benchmarks.

Index Terms

Federated leaning, UAV communications, completion time minimization, device scheduling, and

UAV trajectory design.

I. INTRODUCTION

As the storage and computation capabilities of edge devices keep growing, it becomes more

attractive to process the data locally and push network computation to the edge [1]–[3]. In the

M. Fu is with the Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117583

(e-mail: fumin@u.nus.edu).

Y. Shi and Y. Zhou are with School of Information Science and Technology, ShanghaiTech University, Shanghai 201210,

China (e-mail: {shiym, zhouyong}@shanghaitech.edu.cn).

arXiv:2210.10970v1 [eess.SP] 20 Oct 2022

ﬁeld of machine learning (ML), distributed learning frameworks [4], [5] that keep the training

data locally are well developed to protect data privacy and reduce network energy/time costs.

Recently, federated learning (FL) [1], [4], [5] has been proposed as a promising solution for

distributed ML, which enables multiple devices to execute local training on their own dataset and

collaboratively build a shared ML model with the coordination of a parameter server (PS) (e.g.,

access point and base station). Since only model parameters rather than raw data are exchanged

between devices and the PS, FL signiﬁcantly relieves the communication burden and protects

data privacy [4], [6] with wide-ﬁeld applications, e.g., vehicle-to-vehicle communications [7]

and content recommendations for smartphones [5].

In contrast to the centralized ML, the PS in FL needs to exchange models with multiple devices

over hundreds to thousands of communication rounds to achieve the desired training accuracy.

However, the main challenge in realizing FL on wireless networks arises from communication

stragglers with unfavorable links [8], [9]. For example, in over-the-air computation (AirComp)-

based analog FL [6], [10], communication stragglers dominate the overall model aggregation

error caused by channel fading and communication noise since the devices with better channel

qualities have to reduce their transmit power for the local models’ alignment at the PS. Moreover,

in digital synchronous FL [8], [11], communication stragglers signiﬁcantly slow down the model

aggregation process and dominate cumulative communication delay since the PS must wait until

receiving the training updates from all participants. If the number of communication stragglers

is high, the overall communication delay will be unacceptable. The straggler issue is thus the

main bottleneck to design communication-efﬁcient FL systems.

There have been many efforts to mitigate the communication straggler effect in FL, such as

device scheduling [6], [10], [11]. For instance, to reduce model misalignment error incurred by

stragglers in AirComp-based FL, the authors in [6], [10] scheduled the devices with reliable chan-

nels for concurrent model uploading. In addition, to reduce the communication delay incurred

by stragglers in digital FL, devices with large contributions to the global model [11] or/and with

favorable channel conditions [12], [13] are generally selected. Nevertheless, because such device

scheduling is biased, which results in a smaller amount of training data utilized, this, in turn,

may damage the update of the global model and decrease the learning performance of FL. To

alleviate such communication-learning tradeoff, recent research has investigated the integration

of advanced technologies (i.e., relays [14], reconﬁgurable intelligent surfaces [15]–[17]) into

FL systems to improve stragglers’ communication qualities and thus further upgrade device

scheduling policy for the reduction of communication errors. These existing frameworks require

a terrestrial BS to provide network coverage to the devices for model aggregation. However, many

FL tasks need to be performed under the circumstances when terrestrial networks are unavailable

in remote areas. For example, devices from multiple regions (e.g., forests and woodlands) can

collaborate through FL to build a learning model for ﬁre monitoring [18]. Under these harsh

environments, it is imperative to deploy a more ﬂexible PS that proactively establishes favorable

communication links among devices.

As a viable complementary alternative to terrestrial networks, unmanned aerial vehicles (UAVs)

can provide coverage extension and seamless connectivity to support various FL tasks, especially

in distant and underdeveloped areas [19]–[21]. Inspired by this, this paper studies a UAV-

enabled FL network, where a UAV is dispatched as a ﬂying PS to aggregate and update the

digital FL model parameters when no terrestrial BS is available. To mitigate the communication

straggler effect in UAV-enabled FL networks, we propose to jointly design UAV trajectory

and device scheduling. First, the qualities of communication channels between the UAV and

devices still differ since all links’ channel conditions depend on the UAV’s location at each

time slot. To address this issue, device scheduling is necessary to prevent communication strag-

glers. Furthermore, by utilizing its mobility, the UAV can establish short-distance LoS links

to scheduled devices. As a result, each scheduled device achieves a high data rate for model

uploading, resulting in faster model uploads/downloads per round compared to the static UAV.

In addition, with its ability to dynamically adjust communication distances, the UAV can prevent

any device from being a communication straggler all the time, ensuring that all devices have the

opportunity to participate in FL training. As such, incorporated with UAV trajectory planning,

the optimized device scheduling strategy focuses on data exploitation maximization, thereby

reducing cumulative model aggregation loss and accelerating FL convergence. Hence, such join

design in UAV-enabled FL networks is an appealing solution to address the straggler issue and

reduce communication time.

Motivated by the above observations, in this paper, we focus on the time required for complet-

ing the FL training process [22], [23], which includes not only the computation time but also the

communication time of all scheduled devices. The completion time is a critical design aspect in

UAV-enabled systems, as UAVs usually have a limited endurance due to the practical physical

constraints [24]. Additionally, devices generally have a limited energy budget without battery

replacement or recharging [9]. Thus, the formulated optimization problem needs to consider

not only the FL constraints such as the target convergence accuracy level but also the devices’

dynamic communication conditions such as energy consumption. As such, this paper aims to

minimize the completion time of UAV-enabled FL by jointly optimizing the UAV trajectory,

device scheduling, and time allocation for energy-constrained devices, while ensuring that the

FL algorithm can converge to a target accuracy.

A. Contributions

The main contributions of this paper are summarized as follows.

•We consider a novel UAV-enabled FL framework, where a mobile UAV is dispatched as a

PS to exchange the model parameters with devices, thereby preventing devices from being

communication stragglers. Moreover, under the convergence accuracy of FL constraint, we

mainly focus on the completion time minimization problem for UAV-enabled FL systems.

This consideration is of paramount importance for latency-critical FL applications and

limited endurance UAV systems.

•We ﬁrst derive an upper bound on the iterative norm of the global gradients for non-convex

loss functions, taking model update errors from device selection into account. Speciﬁcally,

the analytical bound shows that the device selection loss causes convergence rate reduction

and leads to a non-diminishing gap between the initial model and the global optimum of

the training loss.

•Based on the convergence bound, we formulate the completion time minimization problem

by jointly designing device scheduling, communication time allocation for scheduled de-

vices, and trajectory planning for UAV, taking into account the target convergence accuracy

of FL, energy budget at devices, and practical constraints at the UAV. Besides, we quan-

titatively analyze the fundamental tradeoff between learning accuracy and communication

latency, and demonstrate the importance of the mobile UAV in the proposed system.

•Although the formulated mixed-integer nonconvex problem is high intractable, we propose

an efﬁcient iterative block coordinate descent (BCD) algorithm to solve the joint device

scheduling and time allocation optimization subproblem and the UAV trajectory optimization

subproblem alternately, which is guaranteed to converge. Moreover, to reduce computational

complexity, each optimization subproblem is solved optimally with a closed-form solution

by applying the Lagrange duality method.

Simulation results in realistic federated settings are provided to illustrate the learning-communication

tradeoff and validate the effectiveness of the proposed scheme. Speciﬁcally, the proposed joint

design scheme outperforms existing benchmark schemes in terms of mission completion time,

which is appealing in light of the limited endurance of UAVs. Moreover, our proposed scheme

provides comparable performance to the full-scheduling ideal benchmark in terms of prediction

accuracy, even when the target convergence accuracy of FL is relatively large.

B. Related Work

1) UAV Assisted FL Networks: Upon the completion of this work, the application of UAV

in FL networks was investigated in some parallel works [25]–[28] Speciﬁcally, the authors in

[25] developed a novel FL framework with UAV swarms to improve the FL learning efﬁciency.

The authors in [26] proposed an FL-based sensing and collaborative learning approach for UAV-

enabled internet of vehicles (IoVs), where UAVs as devices collect data and train ML models for

IoVs. In addition, [27] described using UAVs as ﬂight relays to support wireless communication

between IoVs and the FL server, thus enhancing FL accuracy. The authors in [28] studied the

deployment of multiple UAVs as ﬂying BSs to minimize the weighted sum of FL execution time

and function loss. Nevertheless, this work does not consider device budget issues that may affect

FL performance and convergence cannot be guaranteed.

2) Latency Minimization Problems in FL Networks: A few works have studied the completion

time minimization problems in different FL scenarios. The authors in [22] formulated an FL

framework over a wireless network as an optimization problem that minimizes the sum of

FL aggregation latency and total device energy consumption. In addition, the authors in [29]

investigated the tradeoff between the FL convergence time and devices’ energy consumption.

However, in [22], [29], all devices are assumed to be involved in each round.

C. Organization

The remainder of this paper is organized as follows. Section II describes the FL via the

UAV system model. In Section III, we provide the convergence analysis of FL and completion

time minimization problem formulation. In Section IV, we propose a BCD method to solve the

formulated problem. Section V presents the numerical results to evaluate the performance of the

proposed algorithm. Finally, we conclude this paper in Section VI.

Notations: In this paper, scalars, column vectors and matrices are written in italic letters,

boldfaced lower-case letters and boldfaced upper-case letters respectively, e.g., a,a,A.RM×N

denotes the space of a real-valued matrix with Mrows and Ncolumns. kak2denotes the

Euclidean norm of vector aand aTrepresents its transpose. |S| denotes the cardinality of the

set S.h·,·i represents the inner product.

II. SYSTEM MODEL

We consider a UAV-assisted FL network that consists of a single-antenna UAV and a set Kof

Ksingle-antenna devices, aiming to collaboratively learn an ML model (e.g., logistic regression

and linear regression). Since the terrestrial BSs are usually sparsely deployed or unavailable in

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1FederatedLearningviaUnmannedAerialVehicleMinFu,Member,IEEE,YuanmingShi,SeniorMember,IEEE,andYongZhou,Member,IEEEAbstractToenablecommunication-efcientfederatedlearning(FL),thispaperstudiesanunmannedaerialvehicle(UAV)-enabledFLsystem,wheretheUAVcoordinatesdistributedgrounddevicesforasharedmodeltrain...

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