IEEE Computational Intelligence Magazine - August 2022 - 31

❏ The block generation rate is determined by
the computational complexity of the hash
function and the total computing power of
the blockchain network (i.e., total CPU
cycles). The average CPU cycles required to
generate a block can be defined as kcB
where k denotes the mining difficulty and cB
,
is the average
number of total CPU cycles required to generate a block.
Thus, the average generation time of a block (tB
expressed as kc /NfB
) can be
, where N is the number of clients and f
denotes the CPU cycles per second of each client.
❏ The training time consumed by each training iteration, tT
can be expressed as (| |/ )Dc fT
number of samples of each client and cT
CPU cycles required to train one sample.
,
, where ||D denotes the
is the number of
❏ Considering that a typical FL learning task is required to
be accomplished within a fixed duration of TSum
Kt tTSumTBx +
#
, the total
learning and mining times should be satisfied that
()
, where K denotes the number of total
communication rounds and x the number of local training
epochs. Thus, to achieve required learning performance,
the number of communication rounds K should
be optimized under a certain ratio between the training
and mining time.
C. Lazy Clients
As the verification is processed locally, a lazy client may not
perform local learning and directly copy uploaded parameters
from other clients to save its computing resources. As a result,
the client can devote more mining resources to reaping more
mining rewards with a higher probability. However, this action
degrades learning performance. To investigate the effect of lazy
nodes on the system performance, related experimental results
are provided in Sec. V-D.
To address the lazy client issue, a signature process can be
implemented at each client, which is based on the pseudo-noise
(PN) sequence. The signature in BLADE-FL is resilient to noise
perturbation because the lazy clients are likely to perturb the
plagiarized local models to hide their misbehavior. This process
can improve detection accuracy of lazy clients at the cost of
negligible overhead to the system. The details of the process are
the following.
❏ Before broadcasting the local updates, each client will
produce a PN sequence of length L, where L is usually a
very large number (larger than the number of model
parameters), and a same length with model parameters is
selected and added to the local updates. This PN
sequence has a high self-correlation coefficient and is
difficult to detect or re-produce by other clients. Minimally,
the complexity of detecting the PN sequence
should be much larger than that of training the neural
network so as to deter the attempt to discover the used
PN sequence.
❏ Upon receiving local updates from the other clients, each
client will use its own PN sequence to check the correlaIV.
Experimental Results and Potential Solutions
In this section, several related experimental results are provided
to show the issues in the multi-functional miner in the proposed
BLADE-FL system.
A. System Setup
For each experiment, the original training data is divided into
non-iid training sets, and locally computes a stochastic gradient
descent (SGD) updated on each dataset, and then the
server aggregates updates to train a globally shared classifier.
The prototype is evaluated on the Fashion-MNIST and
Cifar-10 datasets.
ALGORITHM 2 PN Sequence Detection Algorithm.
Data: Number of communication rounds T, number of clients N,
detection threshold m, and amplitude of PN sequence a.
1 Initialize: w0
, t = 1
2 while tT1= do
3
4
if t = 1 then
i-th client adds an additive PN sequence to the
learned model as ww S
X =+a .
i
t
5
6
7
8
9
10
11
12
i
t
i
t
Calculates the cross-correlation value between model
parameters and its own PN sequence as
C Sw Sw S()
ij,
t
== +
X
i
t
)) a
j
t
i
t
j
t
Performs peak detection.
$ m then
wj
t
else
wj
t
is honest.
13 Performs a global update as wwi|| /| |,DDt=RR m
N
Discards models that are detected as lazy clients
X j c
N
i==
`
where Nt is number of honest clients after discarding
lazy clients.
j
14 tt 1=+
Result: wT
i
t
11
tt
j
is copied;
if Cj
t
j
t
.
Sums the cross-correlation value as CC,
,
j
t
= /
1
ii j
N
= !
ij
t
.
tion coefficient with the updates. If high peaks in terms of
the cross-correlation coefficient exist, then the lazy clients
will be detected.
❏ Once a lazy client is recognized by a local client, this client
can publish the previously used PN sequence to others and
invite other honest clients to verify this process. Then, any
future updates from the lazy client might be discarded as
punishments.
The pseudo-code of the PN sequence detection is shown
in Algorithm 2.
To achieve local differential privacy, each client
will add a random noise that follows a certain
distribution on the uploaded models.
AUGUST 2022 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 31
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