Blockchained On-Device Federated Learning

1

Blockchained On-Device Federated Learning

Hyesung Kim, Jihong Park†, Mehdi Bennis†, and Seong-Lyun Kim

Abstract—By leveraging blockchain, this letter proposes ablockchained federated learning (BlockFL) architecture wherelocal learning model updates are exchanged and verified. Thisenables on-device machine learning without any centralizedtraining data or coordination by utilizing a consensus mechanismin blockchain. Moreover, we analyze an end-to-end latency modelof BlockFL and characterize the optimal block generation rate byconsidering communication, computation, and consensus delays.

Index Terms—On-device machine learning, federated learning,blockchain, latency.

I. INTRODUCTION

FUTURE wireless systems are envisaged to ensure lowlatency and high reliability anywhere and anytime [1]–

[3]. To this end, on-device machine learning is a compellingsolution wherein each device stores a high-quality machinelearning model and is thereby capable of make decisions, evenwhen it loses connectivity. Training such an on-device machinelearning model requires more data samples than each device’slocal samples, and necessitates sample exchanges with otherdevices [4]–[6]. In this letter, we tackle the problem of trainingeach device’s local model by federating with other devices.

One key challenge is that local data samples are ownedby each device. Thus, the exchanges should keep the rawdata samples private from other devices. For this purpose, asproposed in Google’s federated learning (FL) [4], [5], referredto as vanilla FL, each device exchanges its local model update,i.e., learning model’s weight and gradient parameters, fromwhich the raw data cannot be derived. As illustrated in Fig. 1-a, the vanilla FL’s exchange is enabled by the aid of a centralserver that aggregates and takes an ensemble average of allthe local model updates, yielding a global model update.Then, each device downloads the global model update, andcomputes its next local update until the global model trainingis completed [5]. Due to these exchanges, the vanilla FL’straining completion latency might be tens of minutes or more,as demonstrated in Google’s keyboard application [7].

The limitation of the vanilla FL operation is two-fold.Firstly, it relies on a single central server, which is vulnerableto the server’s malfunction. This incurs inaccurate globalmodel updates distorting all local model updates. Secondly,it does not reward the local devices. A device having a largernumber of data samples contributes more to the global training.

This work was partly supported by Institute of Information & communicationsTechnology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT)(No.2018-0-00170, Virtual Presence in Moving Objects through 5G), Basic ScienceResearch Foundation of Korea(NRF) grant funded by the Ministry of Science and ICT(NRF-2017R1A2A2A05069810), and the Mobile Edge Intelligence at Scale (ELLIS)project at the University of Oulu.

H. Kim and S.-L. Kim are with School of Electrical and Electronic Engineering,Yonsei University, Seoul, Korea (email: {hskim, slkim}@ramo.yonsei.ac.kr).

†J. Park and †M. Bennis are with the Centre for Wireless Communications, Universityof Oulu, 4500 Oulu, Finland (email: {jihong.park, mehdi.bennis}@oulu.fi).

Federated learning

�1

block propagation

ledger

data rewardBlockchain

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mining reward

block generation

cross verification

(1)

(2)

(3)

(4)

(a) Vanilla FL. (b) Proposed BlockFL.

global model

local data

local model

Fig. 1. An illustration of (a) the vanilla federated learning (FL) [4], [5] and(b) the proposed blockchained FL (BlockFL) architectures.

Without providing compensation, such a device is less willingto federate with the other devices possessing few data samples.

In order to resolve these pressing issues, by leveragingblockchain [8], [9] in lieu of the central server, we propose ablockchained FL (BlockFL) architecture, where the blockchainnetwork enables exchanging devices’ local model updateswhile verifying and providing their corresponding rewards.BlockFL overcomes the single point of failure problem andextends the range of its federation to untrustworthy devices ina public network thanks to a validation process of the localtraining results. Moreover, by providing rewards proportionalto the training sample sizes, BlockFL promotes the federationof more devices with a larger number of training samples.

As shown in Fig. 1-b, the logical structure of BlockFLconsists of devices and miners. The miners can physically beeither randomly selected devices or separate nodes such asnetwork edges (i.e., base stations in cellular networks), whichare relatively free from energy constraints in mining process.The operation of BlockFL is summarized as follows: Eachdevice computes and uploads the local model update to itsassociated miner in the blockchain network; Miners exchangeand verify all the local model updates, and then run the Proof-of-Work (PoW) [8]; Once a miner completes the PoW, itgenerates a block where the verified local model updates arerecorded; and finally, the generated block storing the aggregatelocal model updates is added to a blockchain, also known asdistributed ledger, and is downloaded by devices. Each devicecomputes the global model update from the new block.

Note that the global model update of BlockFL is computedlocally at each device. A miner’s or a device’s malfunctiondoes not affect other devices’ global model updates. For thesake of these benefits, in contrast to the vanilla FL, BlockFLneeds to account for the extra delay incurred by the blockchainnetwork. To address this, the end-to-end latency model ofBlockFL is formulated by considering communication, compu-tation, and the PoW delays. The resulting latency is minimizedby adjusting the block generation rate, i.e., the PoW difficulty.

arX

iv:1

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9v2

[cs

.IT

] 1

Jul

201

9

2

II. ARCHITECTURE AND OPERATION

FL operation in BlockFL: The FL under study is operatedby a set of devices D = {1, 2, · · · , ND} with |D| = ND. The i-thdevice Di owns a set of data samples Si with |Si| = Ni, andtrains its local model. The local model updates of the deviceDi is uploaded to its associated miner Mj that is uniformlyrandomly selected out of a set of miners M={1, 2, · · · ,NM}.

Our distributed model training focuses on solving a regres-sion problem in a parallel manner, considering a set of theentire devices’ data samples S = ∪ND

i=1Si with |S| = NS .The k-th data sample sk ∈ S is given as sk = {xk, yk} fora d-dimensional column vector xk ∈ Rd and a scalar valueyk ∈ R. The objective is to minimize a loss function f(w) for aglobal weight vector w ∈ Rd. The loss function f(w) is chosenas the mean squared error: f(w) = 1

NS

∑ND

i=1

∑sk∈Si fk(w),

where fk(w)=(x>k w− yk)2/2. Other loss functions under deepneural networks can readily be incorporated, as done in [10].

In order to solve the above problem, following the vanillaFL settings in [4], the model of the device Di is locallytrained via a stochastic variance reduced gradient algorithm[4], and all devices’ local model updates are aggregated usinga distributed approximate Newton method. For each epoch,the device Di’s local model is updated with the number Niof iterations. At the t-th local iteration of the `-th epoch, thelocal weight w(t,`)

i ∈ Rd is:

w(t,`)i = w

(t−1,`)i −

β

Ni

([∇fk(w

(t−1,`)i )−∇fk(w(`))

]+∇f(w(`))

), (1)

where β > 0 is a step size, w(`) indicates the global weight atthe `-th epoch, and ∇f(w(`)) = 1/NS ·

∑NDi=1

∑sk∈Si

∇fk(w(`)).Let w(`)

i denote the local weight after the last local iterationof the `-th epoch, i.e., w(`)

i =w(Ni,`)i . Then,

w(`) = w(`−1) +

ND∑i=1

NiNS

(w

(`)i − w

(`−1)). (2)

In vanilla FL in [4], [5], the device Di uploads its localmodel update (w

(`)i , {∇fk(w(`))}sk∈Si ) to the central server,

with the model update size δm that is identically given for alldevices. The global model update (w(`),∇f(w(`))) is computedby the server. In BlockFL, the server entity is substituted witha blockchain network as detailed in the following description.

Blockchain operation in BlockFL: In the BlockFL, theblocks and their verification by the miners in M are de-signed so as to exchange the local model updates truthfullythrough a distributed ledger. Each block in a ledger is dividedinto its body and header parts [8]. In BlockFL, the bodystores the local model updates of the devices in D, i.e.,(w

(`)i , {∇fk(w(`))}sk∈Si ) for the device Di at the `-th epoch, as

well as its local computation time T (`)local,i that is discussed at the

end of this subsection. The header contains the information ofa pointer to the previous block, block generation rate λ, andthe output value of the PoW. The size of each block is set ash + δmND, where h and δm are the header and model updatesizes, respectively. Each miner has a candidate block that isfilled with the local model updates from its associated devicesand/or other miners. The filling procedure continues until itreaches the block size or a waiting time Twait.

1. Local model update

2. Local model upload

3. Cross-verification

4. Block generation5. Block propagation6. Global model download

7. Global model update

M2<latexit 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data reward

mining winner

(a) Without forking. (b) With forking.

mining reward

Forking


M2<latexit 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Fig. 2. The one-epoch operation of BlockFL with and without forking.

Afterwards, following the PoW [8], the miner randomlygenerates a hash value by changing its input number, i.e.,nonce, until the generated hash value becomes smaller thana target value. Once the miner M1 succeeds in finding thehash value, its candidate block is allowed to be a new blockas shown in Fig 2. Here, the block generation rate λ canbe controlled by the PoW difficulty, e.g., the lower PoWtarget hash value, the smaller λ. Due to simpleness androbustness, the PoW is applied to the wireless systems as in[11], [12]. BlockFL can also use other consensus algorithmssuch as the proof-of-stake (PoS) or Byzantine-fault-tolerance(BFT), which may require more complicated operation andpreliminaries to reach consensus among miners.

The generated block is propagated to all other miners. Tothis end, as done in [8], all the miners receiving the generatedblock are forced to stop their PoW operations and to add thegenerated block to their local ledgers. As illustrated in Fig 2,if another miner M2 succeeds in its block generation withinthe propagation delay of the firstly generated block, then someminers may mistakenly add this secondly generated block totheir local ledgers, known as forking. In BlockFL, forkingmakes some devices apply an incorrect global model updateto their next local model updates. Forking frequency increaseswith λ and the block propagation delay, and its mitigationincurs an extra delay, to be elaborated in Sect. III.

The blockchain network also provides rewards for datasamples to the devices and for the verification process tothe miners, referred to as data reward and mining reward,respectively. The data reward of the device Di is received fromits associated miner, and its amount is proportional to the datasample size Ni. When the miner Mj generates a block, itsmining reward is earned by the blockchain network, as donein the conventional blockchain structure [8]. The amount ofmining reward is proportional to the aggregate data sample sizeof its all associating devices, namely, ∑NMj

i=1 Ni where NMj

denotes the number of devices associated with the miner Mj .It is noted that the BlockFL can further be improved usinga reward mechanism, which considers not only the size butalso the quality of data sample that affects the accuracy of FL.Untruthful devices may inflate their sample sizes with arbitrarylocal model updates. Miners verify truthful local updatesbefore storing them by comparing the sample size Ni with itscorresponding computation time T (`)

local,i. This can be guaranteedin practice by Intel’s software guard extensions, allowingapplications to be operated within a protected environment,which is utilized in blockchain technologies [13].

3

One-epoch BlockFL operation: As depicted in Fig. 2,the BlockFL operation of the device Di at the `-th epoch isdescribed by the following seven steps.1. Local model update: The device Di computes (1) with thenumber Ni of iterations.2. Local model upload: The device Di uniformly randomlyassociates with the miner Mi; if M = D, then Mi isselected from M\Di. The device uploads the local modelupdates (w

(`)i , {∇fk(w(`))}sk∈Si ) and the corresponding local

computation time T (`)local,i to the associated miner.

3. Cross-verification: Miners broadcast the obtained localmodel updates. At the same time, the miners verify thereceived local model updates from their associated devices orthe other miners. The verified local model updates are recordedin the miner’s candidate block, until its reaching the block size(h+ δmND) or the maximum waiting time Twait.4. Block generation: Each miner starts running the PoW untileither it finds the nonce or it receives a generated block.5. Block propagation: Denoting as Mo ∈ M the miner whofirst finds the nonce. Its candidate block is generated as anew block and broadcasted to all miners. In order to avoidforking, an ACK, including whether forking occurs or not,is transmitted once each miner receives the new block. If aforking event occurs, the operation restarts from Step 1. Aminer that generates a new block waits until a predefinedmaximum block ACK waiting time Ta,wait.6. Global model download: The device Di downloads thegenerated block from its associated miner.7. Global model update: The device Di locally computes theglobal model update in (2) by using the aggregate local modelupdates in the generated block.The procedure continues until satisfying |w(L)−w(L−1)|≤ε.

Centralized FL is vulnerable to the server’s malfunctionthat distorts all devices’ global models. However, in BlockFL,the global model update is computed locally at each device,which is robust against the malfunction and prevents excessivecomputational overheads of miners.

III. END-TO-END LATENCY ANALYSIS

We investigate the optimal block generation rate λ∗ min-imizing learning completion latency To, defined as the totaltime during L epochs at a randomly selected device Do∈D.

One-epoch BlockFL latency model: The `-th epoch la-tency T (`)

o is determined by computation, communication, andblock generation delays. First, computation delays are broughtby Steps 1 and 7 in Sect. II. Let δd denote a single datasample’s size identical for all data samples. Processing δdwith the clock speed fc requires δd/fc. Local model updatingdelay T

(`)local,o in Step 1 is thus given as T

(`)local,o = δdNo/fc.

Likewise, global model updating delay T(`)global,o in Step 7

is evaluated as T(`)global,o = δmND/fc. Note that δd and δm

change with applications types. Second, communication delaysare entailed by Steps 2 and 6 between devices and miners.Measuring the achievable rate under additive white Gaussiannoise channels, local model uploading delay T

(`)up,o in Step 2

is computed as T(`)up,o = δm/[Wup log2(1 + γup,o)], where Wup

is the uplink bandwidth allocation per device and γup,o is

the miner Mo’s received signal-to-noise ratio (SNR). Theglobal model downloading delay T

(`)dn,o in Step 6 is given as

T(`)dn,o=(h+δmND)/[Wdn log2(1+γdn,o)], where Wdn is the downlink

bandwidth per device and γdn,o is the device Do’s SNR.For Steps 3 and 5, assuming verification processing time

is negligible compared to the communication delays, cross-verification delay T (`)

cross,o in Step 3 is T (`)cross,o=max{Twait−(T

(`)local,o+

T(`)up,o),

∑Mj∈M\Mo

δmNMj/[Wm log2(1 + γoj)]} under frequency

division multiple access (FDMA), where Wm is the bandwidthallocation per each miner link and γoj is the miner Mj’sreceived SNR from the miner Mo. Denoting as Mo ∈ Mthe miner who first finds nonce, referred to as the miningwinner, total block propagation delay T (`)

bp,o in Step 5 is givenas T (`)

bp,o =maxMj∈M\Mo{t(`)bp,j , Ta,wait} under FDMA. The term

t(`)bp,j=(h+δmND)/[Wm log2(1+γoj)] represents the block prop-

agation delay from the mining winner Mo to Mj ∈ M\Mo,and γoj is the miner Mj’s received SNR. Lastly, in Step 4,block generation delay T (`)

bg,j of the miner Mj ∈M follows anexponential distribution with mean 1/λ, as modeled in [9]. Thedelay of interest is the mining winner Mo’s block generationdelay T

(`)bg,o. Finally, the `-th epoch latency T

(`)o is

T(`)o =N

(`)fork

(T

(`)local,o+T

(`)up,o+T

(`)cross,o+T

(`)bg,o+T

(`)bp,o

)+T

(`)dn,o+T

(`)global,o, (3)

where N (`)fork denotes the number of forking occurrences in the

`-th epoch, and follows a geometric distribution with mean1/(1−p(`)fork), with the forking probability p(`)fork at the `-th epoch.Following Step 5, the forking probability is represented as:

p(`)fork = 1−

∏Mj∈M\Mo

Pr(t(`)j − t

(`)o > t

(`)bp,j

), (4)

where the term t(`)j = T

(`)local,j + T

(`)up,j + T

(`)cross,j + T

(`)bg,j is the

cumulated delay until the miner Mj generates a block.Latency optimal block generation rate: Using the one-

epoch latency (3), we derive the optimal block generationrate λ∗ that minimizes the `-th epoch latency averaged overthe PoW process. Here, the PoW process affects the blockgeneration delay T

(`)bg,o, block propagation delay T

(`)bp,o, and the

number N (`)fork of forking occurrences, which are inter-dependent

due to the mining winner Mo. We consider the case where allminers synchronously start their PoW processes by adjustingTwait such that T (`)

cross,o=Twait−(T (`)local,o+T

(`)up,o). In this case, even the

miners completing the cross-verification earlier wait until Twait,providing the latency upper bound. With this approximation,we derive the optimal block generation rate λ∗ as follows.Proposition 1. With the PoW synchronous approximation,i.e., T (`)

cross,o = Twait − (T(`)local,o + T

(`)up,o), the block generation rate

λ∗ minimizing the `-th epoch latency E[T (`)o ] averaged over the

PoW process is given by:

λ∗ ≈ 2

(T

(`)bp,o

[1 +

√1 + 4NM

(1 + Twait/T

(`)bp,o

)])−1

.

Proof: Applying the synchronous PoW approximation and themean 1/(1− p(`)fork) of the geometrically distributed N

(`)fork to (3),

E[T(`)o ] ≈

(Twait + E[T

(`)bg,o]

)/(1− p(`)fork

)+ T

(`)dn,o + T

(`)global,o. (5)

The terms Twait, T(`)dn,o, T

(`)global,o are constant delays given

in Sect. II. For the probability p(`)fork, using (4) with t

(`)j −

4

0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18650

700

750

800

850

900

950

1000

1050

Glo

bal c

ompl

etio

n tim

e (m

s)

�3

Fig. 4

SNR = 10 dB

Lear

ning

com

plet

ion

late

ncy

(sec

)

9 dB

8 dB

Block generation rate (Hz)

(a) With respect to λ. (b) Test accuracy.Fig. 3. Average learning completion latency (a) versus block generationrate λ and (b) test accuracy of BlockFL, Vanilla FL, and standalone withoutfederation (γup,o = γdn,o = γoj = SNR).

t(`)o = T

(`)bg,j − T

(`)bg,o under the synchronous approximation,

we obtain p(`)fork as: p

(`)fork = 1 − e

λ∑

Mj∈M\MoT

(`)bp,j , where

T(`)bp,j is a constant delay given in Sect. II-A. Next, for

the delay E[T(`)bg,o], using the definition of T

(`)bg,o and the

complementary cumulative distribution function (CCDF) ofthe exponentially distributed T

(`)bg,j , we derive T

(`)bg,o’s CCDF

as: Pr(T

(`)bg,o > x

)=∏NM

j=1 Pr(T

(`)bg,j > x

)=e−λNMx. Applying

the total probability theorem yields E[T(`)bg,o] = 1/(λNM ). Fi-

nally, combining all these terms, (5) is recast as: E[T(`)o ] ≈

(Twait + 1/λNM )eλ∑

Mj∈M\MoT

(`)bp,j+T

(`)dn,o+T

(`)global,o, which is con-

vex for λ. The optimum λ∗ is thus directly derived. �For a larger λ, the forking event occurs more frequently,

increasing the learning completion latency. On the contrary,for a high PoW difficulty with a low λ, the block generationtime incurs its own overheads with excessive latency.

IV. NUMERICAL RESULTS AND DISCUSSION

We numerically evaluate the proposed blockFL’s averagelearning completion latency E[To] =

∑L`=1 E[T

(`)o ]. By default,

we consider ND = NM = 10, and Ni ∼ Uni(10, 50) ∀Di ∈ D.Following the 3GPP LTE Cat. M1 specification, we use Wup =

Wdn =Wm = 300 KHz and γup,o = γdn,o = γoj = 10 dB. Othersimulation parameters are given as: δd =100 Kbit, δm =5 Kbit,h=200 Kbit, fc=1 GHz, Twait =50 ms, Ta,wait =500 ms.

Fig. 3-a shows the impact of block generation rate λ on theBlockFL’s average learning completion latency. In Fig. 3-a, weobserve that the latency is convex-shaped and is decreasingwith the SNRs. For the optimal block generation rate λ∗,the minimized average learning completion latency obtainedfrom Proposition 1 is always longer by up to 1.5% than thesimulated minimum latency. In Fig. 3-b, the BlockFL and thevanilla FL achieve almost the same accuracy for an identicalND. On the other hand, the learning completion latency of ourBlockFL is lower than that of the vanilla FL (NM =1) as inFig. 4-a, which shows the scalability in terms of the numbersNM and ND of miners and devices, respectively. The averagelearning completion latency is computed for NM = 1, 10

with or without the miners’ malfunction. The malfunctionis captured by adding Gaussian noise N (−0.1, 0.01) to eachminer’s aggregate local model updates with probability 0.05.Without malfunction, a larger NM increases the latency due tothe increase in their cross-verification and block propagationdelays. In BlockFL, each miner’s malfunction only distortsits associated device’s global model update. Such distortion

Fig. 4. Average learning completion latency versus the number of devices,(a) under the miners’ malfunction, (b) for different energy constraints θe, and(c) overtake probability with respect to the number of chained blocks.

can be restored by federating with other devices that associatewith the miners operating normally. Hence, a larger NM mayachieve a shorter latency for NM =10 with the malfunction.

Fig. 4-a shows that there exists a latency-optimal numberND of devices. A larger ND enables to utilize a larger amountof data samples, whereas it increases each block size and blockexchange delays, resulting in the convex-shaped latency.

In Fig. 4-b, we assume that some miners cannot participateif their battery level is lower than a predefined thresholdvalue θe, a normalized battery level, θe ∈ [0,1]. Without themalfunction of miner nodes, the learning completion latencybecomes larger for a lower θe due to an increase in cross-verification and block propagation delays. On the contrary,when the malfunction occurs, a lower θe achieves a shorterlatency because more miners federate with leading to robustglobal model updates. Fig. 4-c shows the overtake probabilitythat a malicious miner will ever form a new blockchain whoselength is longer than a blockchain formed by honest miners.The overtake probability goes to zero if just a few blockshave already been chained by honest miners. Although themalicious miner begins the first PoW with the honest miners,the larger number of miners prevents the overtake.

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