FedDuA sets each round's global learning rate to the average squared client-update norm divided by the aggregated update norm under an adaptive coordinate preconditioner, a rule that is minimax-optimal under an approximate projection condition and convergent for convex objectives.
Here, we used the induction hypothesis for the first inequality and strong A.P.C
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FedDuA: Doubly Adaptive Federated Learning
FedDuA sets each round's global learning rate to the average squared client-update norm divided by the aggregated update norm under an adaptive coordinate preconditioner, a rule that is minimax-optimal under an approximate projection condition and convergent for convex objectives.