FedSAM and FedASAM (Sharpness-Aware Minimization and Server Stochastic Weight Averaging for Federated Learning)

A sharpness-aware federated optimization framework (Caldarola, Caputo, & Ciccone 2022, Sections 3-4, Equations 1-5, Algorithm 1) that mitigates sharp-landscape misalignment across statistically heterogeneous clients by replacing local client SGD with Sharpness-Aware Minimization (FedSAM, perturbing local weights by epsilon^hat_k(w) = rho * grad L_k(w) / ||grad L_k(w)||_2, Equation 3) or Adaptive Sharpness-Aware Minimization (FedASAM, using scale-invariant normalization operator T_w^i = diag(|w|) so epsilon^tilde_k(w) = rho * T_w^2 grad L_k(w) / ||T_w grad L_k(w)||_2, Equation 5), combined on the server side with cyclic-learning-rate Stochastic Weight Averaging (SWA, w_SWA <- (w_SWA * n_models + w^{t+1}) / (n_models + 1) every c rounds starting at fraction s of total rounds, Algorithm 1).