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Bilevel Optimization has witnessed notable progress recently with newemerging efficient algorithms, yet it is underexplored in the FederatedLearning setting. It is unclear how the challenges of Federated Learning affectthe convergence of bilevel algorithms. In this work, we study Federated BilevelOptimization problems. We first propose the FedBiO algorithm that solves thehyper-gradient estimation problem efficiently, then we propose FedBiOAcc toaccelerate FedBiO. FedBiO has communication complexity $O(\epsilon^{-1.5})$with linear speed up, while FedBiOAcc achieves communication complexity$O(\epsilon^{-1})$, sample complexity $O(\epsilon^{-1.5})$ and also the linearspeed up. We also study Federated Bilevel Optimization problems with locallower level problems, and prove that FedBiO and FedBiOAcc converges at the samerate with some modification.

Communication-Efficient Federated Bilevel Optimization with Local and Global Lower Level Problems