| Input: Machine learning algorithm L, client set C = {C1,C2,…,Cn}, local dataset D = {D1,D2,…,Dn}, server set S = {S1,S2,…,Sm}, number of server nodes t′ (2 ≤ t′ < m) that can tolerate collusion, minimum number of clients K for uploading parameters per round, total number of training rounds R |
| Output: Trained model M |
| 01: | S1 initializes the global model M |
| 02: | for r ← 1 to R |
| 03: | for Ci∈C do |
| 04: | if r = 1 |
| 05: | Download the initial global model M from S1 |
| 06: | else |
| 07: | Download the share M*,jr−1 from Si,j ∈{1,2,…,m} |
| 08: | Mr−1←SecRec(M*,jr−1,⋯,M*,mr−1) |
| 09: | end-if |
| 10 | local training Mir←(Mr−1,Di) |
| 11: | clipping weights Mir/max(1,| Mir |/C) |
| 12: | adding noise Mir←Mir+noise(ε,δ,C,K) |
| 13: | t ← t′ + 1 |
| 14: | computing shares (Mi,1r,⋯,Mi,mr)←SecShr(Mi,m,tr) |
| 15: | send Mi,jr to Si,j |
| 16: | end-for |
| 17: | for Sj ∈S do |
| 18: | wait until enough parameters are collected to update the parameters |
| 19: | aggregate share M*,jr←(Mi1,jr+⋯+MiK,jr)/K |
| 20: | end-for |
| 21: | end-for |
| 22: | download shares M*,jR, recover MR |
| 23: | output MR |