Algorithm 1 FedAvg [210]

Input:

$N_{\mathrm{global}}$: Maximum number of global iterations, n: The total number of participating clients, m: The number of clients used in each global iteration, $N_{\mathrm{local}}$: The number of local epochs, and $\eta$: The local learning rate.

Output:

Global model weight $w_G$

Processing:

1: [Central Server]

2: Initialize $w_G^0$

3: for each iteration t from 1 to $N_{\mathrm{global}}$ do

4:  ${\mathcal{M}}_t$ includes m clients randomly selected from the n clients

5:  for each client $i\in {\mathcal{M}}_t$ in parallel do

6:   $w_i^t,N_i\leftarrow \mathrm{LocalTraining}(i,w_G^t)$

7:  end for

8:  $w_G^{t+1}=\frac{1}{{\sum }_{j=1}^m{N}_j}{\sum }_{i=1}^m{N}_i{w}_i^t$

9: end for

10: [Each Participating Client]

11: $\mathrm{LocalTraining}(i,w)$:

12: ${\mathcal{B}}_i$ is the set of batches for the local dataset ${\mathcal{D}}_i$

13: for each epoch j from 1 to $N_{\mathrm{local}}$ do

14:  for each batch $b\in {\mathcal{B}}_i$ do

15:   $w\leftarrow w-\eta \nabla L(w;b)$

16:  end for

17: end for

18: return the weights $w$ and $N_i=\left|{\mathcal{D}}_i\right|$