Papers › Gradient Tracking for High Dimensional Federated Optimization
Gradient Tracking for High Dimensional Federated Optimization
Jiadong Liang, Yang Peng, Zhihua Zhang
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In this paper, we study the (decentralized) distributed optimization problem with high-dimensional sparse structure. Building upon the FedDA algorithm, we propose a (Decentralized) FedDA-GT algorithm, which combines the \textbf{gradient tracking} technique. It is able to eliminate the heterogeneity among different clients' objective functions while ensuring a dimension-free convergence rate. Compared to the vanilla FedDA approach, (D)FedDA-GT can significantly reduce the communication complexity, from O(s²logd/ε^(3/2)) to a more efficient O(s²logd/ε). In cases where strong convexity is applicable, we introduce a multistep mechanism resulting in the Multistep ReFedDA-GT algorithm, a minor modified version of FedDA-GT. This approach achieves an impressive communication complexity of O(slogd log1/ε) through repeated calls to the ReFedDA-GT algorithm. Finally, we conduct numerical experiments, illustrating that our proposed algorithms enjoy the dual advantage of being dimension-free and heterogeneity-free.
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