1 Privacy-preserving Intelligent Resource Allocation for Federated Edge Learning in Quantum Internet

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Privacy-preserving Intelligent Resource Allocation

for Federated Edge Learning in Quantum Internet

Minrui Xu, Dusit Niyato, Fellow, IEEE, Zhaohui Yang, Zehui Xiong, Jiawen Kang*,

Dong In Kim, Fellow, IEEE, and Xuemin (Sherman) Shen, Fellow, IEEE

Abstract—Federated edge learning (FEL) is a promising

paradigm of distributed machine learning that can preserve data

privacy while training the global model collaboratively. However,

FEL is still facing model conﬁdentiality issues due to eavesdrop-

ping risks of exchanging cryptographic keys through traditional

encryption schemes. Therefore, in this paper, we propose a

hierarchical architecture for quantum-secured FEL systems with

ideal security based on the quantum key distribution (QKD) to

facilitate public key and model encryption against eavesdropping

attacks. Speciﬁcally, we propose a stochastic resource allocation

model for efﬁcient QKD to encrypt FEL keys and models. In

FEL systems, remote FEL workers are connected to cluster

heads via quantum-secured channels to train an aggregated

global model collaboratively. However, due to the unpredictable

number of workers at each location, the demand for secret-

key rates to support secure model transmission to the server is

unpredictable. The proposed systems need to efﬁciently allocate

limited QKD resources (i.e., wavelengths) such that the total cost

is minimized in the presence of stochastic demand by formulating

the optimization problem for the proposed architecture as a

stochastic programming model. To this end, we propose a fed-

erated reinforcement learning-based resource allocation scheme

to solve the proposed model without complete state information.

The proposed scheme enables QKD managers and controllers to

train a global QKD resource allocation policy while keeping their

private experiences local. Numerical results demonstrate that the

proposed schemes can successfully achieve the cost-minimizing

objective under uncertain demand while improving the training

efﬁciency by about 50% compared to state-of-the-art schemes.

Index Terms—Federated edge learning, quantum key distri-

bution (QKD), resource allocation, deep reinforcement learning

I. INTRODUCTION

ARTIFICIAL Intelligence (AI) enables a wide range of

computing and networking applications in edge net-

works, e.g., smart cities [1], [2], [3], Internet of Vehicles [4],

Minrui Xu and Dusit Niyato are with the School of Computer Science

and Engineering, Nanyang Technological University, Singapore (e-mail: min-

rui001@e.ntu.edu.sg; dniyato@ntu.edu.sg); Zhaohui Yang is with the College

of Information Science and Electronic Engineering, Zhejiang University,

Hangzhou 310007, China, and Zhejiang Provincial Key Lab of Information

Processing, Communication and Networking (IPCAN), Hangzhou 310007,

China, and also with Zhejiang Laboratory, Hangzhou 31121, China. (e-mail:

zhaohuiyang92@gmail.com); Zehui Xiong is with the Pillar of Information

Systems Technology and Design, Singapore University of Technology and

Design, Singapore 487372, Singapore (e-mail: zehui xiong@sutd.edu.sg);

Jiawen Kang is with the School of Automation, Guangdong University of

Technology, China (e-mail: kavinkang@gdut.edu.cn). Dong In Kim is with the

Department of Electrical and Computer Engineering, Sungkyunkwan Univer-

sity, Suwon 16419, South Korea (e-mail: dikim@skku.ac.kr); Xuemin (Sher-

man) Shen is with the Department of Electrical and Computer Engineer-

ing, University of Waterloo, Waterloo, ON, Canada, N2L 3G1 (e-mail:

sshen@uwaterloo.ca). (*Corresponding author: Jiawen Kang)

[5], and Metaverses [6], [7], [8]. As one of the critical

technologies in AI, federated edge learning (FEL) is a novel

paradigm of privacy-preserving machine learning (ML) for

intelligent edge networks [9]. In FEL, multiple data owners

(a.k.a., FEL workers) can train a global model collaboratively

for a model owner without exposing their sensitive raw data.

To ensure the security of data and models in FEL systems,

many modern cryptographic schemes are applied [10], such

as secure multi-party computation (MPC), trusted execution

environment (TEE), and safe key distribution. For instance,

a secure and trusted collaborative edge learning framework

is proposed in [11], where homomorphic encryption (HE)

and blockchain are leveraged to track and choke malicious

behaviors. With the rapidly increasing computation power of

quantum computers [12], novel techniques will be brought

to empower FEL systems, including large-scale searching,

optimization and semantic communication. However, the FEL

systems based on existing schemes are under serious security

threats. For example, traditional key distribution schemes

based on the hardness in computing of certain mathematical

problems are no longer considered to be safe in the post-

quantum era [10]. Fortunately, based on the quantum no-

cloning theorem [13] and the Heisenberg’s uncertainty prin-

ciple [14], quantum key distribution (QKD) [15] is promis-

ing for providing proven secure key distribution schemes

for collaborative training between FEL workers and model

owners by facilitating public key and model encryption against

eavesdropping attacks.

Originated from classical QKD schemes such as Bennett-

Brassard-1984 (BB84) [16] and Grosshans-Grangier-2002

(GG02) [17], some modern QKD schemes have paved the way

for the Quantum Internet [18] in recent years. For example,

the measurement device-independent QKD (MDI-QKD) [19]

provides one of the practical QKD solutions by increasing the

range of secure communications and ﬁlling the detection gaps

with an untrusted relay by avoiding any eavesdropping attacks

on the Quantum Internet. Although several existing works fo-

cus on the theoretical and experimental aspects of the deploy-

ments of MDI-QKD, the problems of QKD resource allocation

in the Quantum Internet have been largely overlooked [20].

For example, in [21], a deterministic programming model and

a heuristic approach based on the shortest path algorithm are

proposed to optimize the deployment cost of QKD resources.

However, the problem of optimal allocation of QKD resources

for quantum-secured FEL systems with heterogeneous data

and model owners remains open. In particular, the number of

participating FEL workers at different locations and times is

arXiv:2210.04308v1 [cs.NI] 9 Oct 2022

uncertain due to unpredictable node and device failures [22].

Therefore, different security levels might be required by cluster

heads to encrypt local models during global aggregation.

Speciﬁcally, the secret-key rate for reaching the information-

theoretic security (ITS) requirement is dynamic to support

the encryption of intermediate model and related information

according to uncertainties in quantum-secured FEL systems.

To address these uncertainty issues, we propose a stochastic

QKD resource (i.e., wavelength) allocation model to optimize

the QKD deployment cost of the Quantum Internet. To protect

FEL models and public keys from eavesdropping attacks, we

propose a hierarchical architecture for quantum-secured FEL

systems that includes the FEL layer, the control and manage-

ment layer, and the QKD infrastructure layer. To handle the

dynamics of security demands from the FEL layer, we model

the QKD resource allocation of QKD managers and QKD

controllers in the control and management layer as a stochastic

programming model that allocates QKD resources from the

QKD infrastructure layer to cluster heads in the FEL layer.

However, the proposed stochastic model can hardly be applied

in practice because it requires complete state information

from FEL nodes and QKD nodes, which is infeasible for

QKD managers and controllers to collect due to privacy

concerns [23]. Fortunately, the independent QKD resource

allocation problems can be addressed by the promising deep

reinforcement learning (DRL) algorithms [24]. Nevertheless,

the efﬁciency and stability of learning-based approaches still

face the issues of “data islands” during their training and

inference [23]:

•Initially, QKD managers and controllers conﬁgure QKD

nodes to provide QKD resources based only on practical

observation of the state of the FEL layer. However, the

experiences, including observations, actions, and rewards,

are kept in the local replay buffers due to privacy con-

cerns. Therefore, the lack of collaboration between QKD

managers and controllers makes QKD resource allocation

problems more challenging to satisfy changing security

demands in quantum-secured FEL systems.

•Furthermore, QKD managers are reluctant to share their

rewards from the FEL layers directly with QKD con-

trollers. Therefore, QKD controllers can only collect

incomplete experiences, including states and actions, dur-

ing their interaction with the FEL systems, which are

insufﬁcient for their local policy improvement. Therefore,

QKD controllers can only use policies shared by QKD

managers to instruct QKD resource allocation decisions

independently to QKD nodes for the FEL layers.

These issues could lead to inadequate training efﬁciency and

unstable inference performance for learning-based algorithms

in privacy-preserving environments.

To overcome the aforementioned issues, in this paper, we

propose a learning-based QKD resource allocation scheme

for quantum-secured FEL systems, which is strengthened by

federated reinforcement learning. In particular, we use the

model-free off-policy soft actor-critic (SAC) [25] structure to

learn the optimal QKD resource allocation strategy. For each

QKD manager and each controller, a policy network is adopted

to conﬁgure the QKD nodes by learning the allocation strategy

during the interaction with quantum-secured FEL systems.

Moreover, a Q-network is adopted as a critic of each QKD

manager and controller to evaluate the state-action values of

its local policy, i.e., the performance with the local policy.

To avoid direct reward sharing, QKD managers encrypt the

Q-networks and then share them with QKD controllers for

their local policy evaluation and improvement. In this way, the

incomplete experience issues of QKD controllers can be ad-

dressed, thus improving the training efﬁciency of agents in the

control and management layer. In addition, to further improve

convergence efﬁciency, the local policy of QKD controllers

is aggregated as the global QKD resource allocation policy

for QKD managers after improving the local policies of QKD

controllers. Our contributions can be summarized as follows.

•We propose a new hierarchical architecture for quantum-

secured FEL systems to resolve uncertain factors in

global model aggregation while providing ITS transmis-

sion of public keys and models. This architecture is

capable of protecting the transmission of FEL models

from external and participant attacks.

•In the proposed architecture, unlike deterministic linear

programming, we formulate the optimization problem as

stochastic programming to resolve the uncertainty of the

security demand in quantum-secured FEL systems, i.e.,

the required secret-key rates. Considering the dynamic

factors in the global aggregation of FEL, such as the

number of FEL workers, the proposed model aims to

minimize the deployment cost of the systems.

•To solve the proposed stochastic model without complete

information, we proposed a federated DRL scheme that

allows QKD managers and controllers to make the op-

timal decision independently based only on their local

partial observation. Speciﬁcally, the proposed scheme

enables QKD managers and controllers to learn a global

policy collaboratively while maintaining their experiences

in local replay buffers. Therefore, the proposed scheme

can learn a synthetic QKD resource allocation policy

efﬁciently without prior knowledge while preserving the

privacy of the learning agents.

•Extensive experiments demonstrate the effectiveness of

stochastic and learning-based resource allocation schemes

for quantum-secured FEL systems. The performance eval-

uation results illustrate that existing baselines in the

Quantum Internet with average or random demand do not

lead to acceptable solutions that are signiﬁcantly inferior

to the proposed schemes.

We organize the rest of this paper as follows. In Section II,

we provide a review of the related works. In Section III,

we discuss the system model. In Section IV, we discuss the

proposed optimization solution approach. In Section V, we

propose the federated deep learning-based algorithm. Finally,

we conduct the simulation experiments in Section VI and

conclude in Section VII. The abbreviations and deﬁnitions

used in this paper are summarized in Table I.

II. RELATED WORKS

A. Federated Edge Learning

Due to the enormous volume of data generated at the

network edge [26], [27], [28], FEL has emerged as a promis-

ing paradigm of distributed privacy-preserving learning to

improve the efﬁciency and security of communication and

sensing for edge networks [29], [30], [31]. To illustrate the

effectiveness and efﬁciency of FEL, Xu et al. in [32] pro-

vided a systematic overview for the convergence of edge

networks and learning. They highlight the potential beneﬁts

of learning-based communication systems, such as semantic

communications, and the necessity of sustainable resource

allocation for edge learning systems. For instance, Hardy et

al. [33] proposed a two-stage federated end-to-end learning

system with performance comparable to centralized learning

systems, including privacy-preserving local dataset adaptation

and federated logistic regression over intermediate results en-

crypted with additive homomorphic encryption (HE) schemes.

To address the problems of multi-view sensing observations in

distributed wireless sensing, Liu et al. [34] proposed a vertical

FEL system for cooperative detection while preserving the

data privacy of sensors. By considering the non-cooperative

nature of FEL participants at the edge, Lim et al. [35]

proposed a hierarchical framework, including the evolutionary

game and the Stackelberg game, for edge association and

resource allocation problems in FEL systems. In addition,

to motivate data owners to participate in FL, Zhan et al.

in [36] provided a comprehensive survey on how to design

proper incentive mechanisms for different federated learning

algorithms in heterogeneous edge networks. Considering that

conventional key distribution schemes in secure FEL systems

are no longer secure, Huang et al. [10] proposed a new

architecture for federated learning systems in the Quantum

Internet called StarFL, which uses satellite and quantum key

distribution schemes to distribute public keys for FEL workers

with provable security.

B. The Quantum Internet

The Quantum Internet [18] connects quantum devices

through quantum channels to provide long-term protection

and future-proof security for the transmission of conﬁdential

information. It is expected that the Quantum Internet can

provide new networking technologies for numerous critical

applications by fusing quantum signal transmission with the

classical communication channels. Aiming to provide se-

cure connectivity for mission-critical applications in the real

world, Toudeh-Fallah et al. [37] established the ﬁrst 800-Gbps

quantum-secured optical channel up to 100 km, which is able

to secure 258 data channels under AES-256-GCM with the

quantum key update rate of one per second. By combining

700 ﬁber-based QKD links and two high-speed satellite-based

QKD links, Chen et al. [38] developed an integrated space-to-

ground quantum communication network with total coverage

of 4,600 km. However, the costly quantum devices and the

non-scalable routing schemes are obstacles to the large-scale

deployment of the Quantum Internet. To address the scalability

issues, Mehic et al. [39] proposed a routing protocol for

TABLE I: Abbreviations and deﬁnitions.

Abbreviations Deﬁnitions

FEL Federated Edge Learning

QKD Quantum Key Distribution

AI Artiﬁcial Intelligence

MPC Multi-party Computation

TEE Trusted Execution Environment

HE Homomorphic Encryption

BB84 Bennett-Brassard-1984

GG02 Grosshans-Grangier-2002

MDI-QKD Measurement Device-Independent QKD

ITS Information-Theoretic Security

DRL Deep Reinforcement Learning

SAC Soft Actor-Critic

KM Key Management

GKS Global Key Server

LKM Local Key Manager

QTs Quantum Transmitters

QRs Quantum Receivers

SIs Security Infrastructures

MUX/DEMUX Multiplexing/Demultiplexing

POMDP Partially Observable Markov Decision Process

SAC Soft Actor-Critic

QBN QKD Backbone Networking

EVF Expected Value Formulation

SIP Stochastic Integer Programming

the Quantum Internet that considers geographic distance and

connection state to achieve high scalability by minimizing

cryptographic key consumption. Meanwhile, For quantum-

secured communications over backbone networks, Cao et

al. [40] developed a programming-based resource allocation

model and a heuristic algorithm to address the deployment

cost-minimized problem efﬁciently.

C. Learning-based QKD Resource Allocation Schemes

Quantum key distribution is one of the mature applications

of the Quantum Internet that has already been applied in some

commercial scenarios [37]. However, QKD resources in the

Quantum Internet still require efﬁcient allocation schemes to

bridge the gap between the low key generation rate of the

Quantum Internet and the uncertain key demands of quantum-

secured communication services. To ﬁll this gap, Zuo et

al. [41] proposed a reinforcement learning-based algorithm

to learn the optimal QKD resource allocation strategy for

management of the quantum key pool in a cost-effective way.

To address the dynamic arrival problem in multi-tenant QKD

deployment, Cao et al. [42] proposed a reinforcement learning-

based algorithm to reduce the deployment cost of QKD

resources. However, these learning-based approaches consider

QKD managers and controllers can share their observations

and experiences without privacy concerns, which is infeasible

in privacy-preserving systems. Therefore, in this paper, we

propose a privacy-preserving learning-based resource alloca-

tion to minimize the deployment cost under uncertain security

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1Privacy-preservingIntelligentResourceAllocationforFederatedEdgeLearninginQuantumInternetMinruiXu,DusitNiyato,Fellow,IEEE,ZhaohuiYang,ZehuiXiong,JiawenKang*,DongInKim,Fellow,IEEE,andXuemin(Sherman)Shen,Fellow,IEEEAbstractFederatededgelearning(FEL)isapromisingparadigmofdistributedmachinelearningthat...

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