Algorithm 1 FedMed. p is the size of workers for training, E is the size of local epochs; the U workers are indexed by u, and $\mathcal{S}$ indicates the choice of adaptive aggregation or FedAvg.

1: procedure SERVERUPDATE: 2:    Initialize $w_0$ 3:    for each round $k=1,2,\dots$ do 4:        $p\leftarrow$ max $(1,C·K)$ 5:        $U_k\leftarrow$ (random p workers) 6:        for each worker $u\in U_k$ in parallel do 7:           $w_{t+1}^u\leftarrow$ WorkerUpdate $(u,w_t)$ 8:        end for 9:        //Implement mediation incentive scheme 10:        $\Delta \leftarrow$ alteration of two losses 11:        $S\leftarrow Se(\Delta )$ 12:        if $S$ is 1 then 13:           $w_{t+1}\leftarrow$Adaptive aggregation 14:         else 15:           $w_{t+1}\leftarrow {\mathsf{\Sigma }}_{u=1}^p\frac{n_u}{n}{w}_{t+1}^u$ 16:        end if 17:    end for 18: end procedure

19: procedure WorkerUpdate($u,w$) 20:    //Run on worker u 21:    $\mathcal{B}\leftarrow$ (split data ${\mathcal{P}}_u$ into batches size of B) 22:    for each local epoch i from 1 to $\mathcal{E}$ do 23:        for batch $b\in \mathcal{B}$ do 24:           $w\leftarrow w-\eta \nabla \mathcal{L}\left(w\right)$ 25:        end for 26:    end for 27:     return w to server 28: end procedure