Algorithm 1.

Adaptive client selection enabling federated learning (ACSFed). K clients are selected from N clients with fraction c; η is the learning rate, P is the probability matrix; H is the cumulative model strength matrix.

Central Server:

Initialize model ω0, P and H

K←max(c·N, 1)

while t in total communication rounds do:

if t=0:

client_set = {randomly selected K clients}

else:

client_set = {select K clients based on probability matrix P}

for each client i in client_set parallel do:

Transmit ωt to client i

Receive ${\omega }_{t+1}^i,\left|\right|los{s}_i|{|}_2^2$, emdi from client i

end for

$H_i\leftarrow f(\left|\right|los{s}_i|{|}_2^2,em{d}_i)$

P←g(P, H)

end while

Distributed Client:

Receive model ωt from the central server

Calculate emdi based on local data distribution

Initialize loss list lossi = {}

Θ← {split local data into batches with size B}

for local epoch 1,2,…, E do:

for θ∈Θ do:

Add training loss toloss

ωt←ωt-η∇g(ωt, θ)

end for

end for

${\omega }_{t+1}^i\leftarrow {\omega }_t$

Calculate$\left|\right|los{s}_i|{|}_2^2$

Transmit ${\omega }_{t+1}^i\left|\right|los{s}_i|{|}_2^2$ and emdi to Central Server