FedDC (Federated Learning via Local Drift Decoupling and Correction)

A primal-dual drift-decoupling and gradient-correction federated learning algorithm (Gao et al. 2022, Section 4, Equations 3-8, Appendix B Algorithm 1 and Theorem 1) that introduces an auxiliary local drift variable h_i ~ w - theta_i for each client i to bridge the parameter gap between the global model w and the local model theta_i, training each active client on the three-term objective F_i(theta_i) = L_i(theta_i) + (alpha/2)*||theta_i - (w - h_i)||^2 + (1/(eta*K))*<theta_i, g_i - g> (Equation 4) where g_i = theta_i^K - theta_i^0 tracks the local epoch update drift and g = sum_i (|D_i|/|D|) g_i, updating h_i^+ = h_i - g_i^+ without extra backpropagation (Equation 6), and aggregating drift-corrected client parameters on the server via w^{t+1} = sum_{i in C_t} (|D_i|/|D|) (theta_i^+ + h_i^+) (Equation 7).