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Federated learning (FL) aims to minimize the communication complexity oftraining a model over heterogeneous data distributed across many clients. Acommon approach is local methods, where clients take multiple optimizationsteps over local data before communicating with the server (e.g., FedAvg).Local methods can exploit similarity between clients' data. However, inexisting analyses, this comes at the cost of slow convergence in terms of thedependence on the number of communication rounds R. On the other hand, globalmethods, where clients simply return a gradient vector in each round (e.g.,SGD), converge faster in terms of R but fail to exploit the similarity betweenclients even when clients are homogeneous. We propose FedChain, an algorithmicframework that combines the strengths of local methods and global methods toachieve fast convergence in terms of R while leveraging the similarity betweenclients. Using FedChain, we instantiate algorithms that improve upon previouslyknown rates in the general convex and PL settings, and are near-optimal (via analgorithm-independent lower bound that we show) for problems that satisfystrong convexity. Empirical results support this theoretical gain over existingmethods.

FedChain: Chained Algorithms for Near-Optimal Communication Cost in Federated Learning