Algorithm 3 Dynamic Asynchronous Federated Averaging (FedDasync)

01. Server Process:

02. Input: $\alpha \in (0,1)$

03. Initialize the global model: $w_0,{\alpha }_t\leftarrow \alpha ,{\beta }_k\leftarrow \frac{D_k}{D}$

04. Scheduler Thread:

05. Scheduler periodically triggers some training tasks on some clients, and sents them

06. from the latest global model with time stamp.

07. Updater Thread:

08. for each round $t=1,2\dots$ do

09.     $\theta =KMeans(\mathrm{timeList},K)$

10.     loop for $\theta$ dynamic seconds after receiving update

11.     Receive the pair $\left(x_{new},\tau \right)$ from any client

12.     timeList.append $(t-\tau )$

13.     ${\gamma }_t\leftarrow \alpha \times S(t-\tau )\times {\beta }_k,S(\cdot )$ is function of stateness

14.     $x_t=\left(1-{\gamma }_t\right)x_{t-1}+{\gamma }_t{x}_{new}$

15.     end loop

16.     $x_t\leftarrow {\displaystyle \sum _{k=1}^K\frac{n}{n_k}}{x}_t^k$

17. end for