Algorithm 1. Adaptive Federated Learning Algorithm with Divergence Estimation and Weight Calculation.

Input: Global model parameters ωt Local datasets for each client Di Local learning rate schedule for each client ηi(t) Output: Updated global model parameters ωt+1 //Client-Side: 1: for each client i in parallel do 2:   for each epoch e do 3:   Train local copy of ωt on Di using ηi(t) 4:   Obtain ${\omega }_i^{\left(t+1\right)}$ 5:   end for 6:     Calculate local performance metrics on ${\omega }_i^{\left(t+1\right)}$ and Di 7:     Estimate divergence between Pi (client’s data distribution) and Pt (global model distribution) using         the Kullback–Leibler (KL) divergence (Equation (2)): 8:      if divergence is acceptable then 9:       Calculate importance weight ${\alpha }_i^{\left(t\right)}$ based on divergence estimation: 10:    else 11:      Adjust learning rate ηi(t) and retrain local model 12: end if 13: end for //Server-Side: 14: Sample clients with probability proportional to ${\alpha }_i^{\left(t\right)}$ 15: Collect ${\omega }_i^{\left(t+1\right)}$ from selected clients 16: Aggregate updates using weighted average (Equation (4)) with ${\alpha }_i^{\left(t\right)}$ as weights: 17: Update the global model using (Equation (5)). 18: if the global model converges then 19:     Broadcast ωt+1 to all clients 20: else 21:     Repeat the process for the next round 22: end if    Updated global model parameters ωt+1