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We consider decentralized model training in tiered communication networks.Our network model consists of a set of silos, each holding a vertical partitionof the data. Each silo contains a hub and a set of clients, with the silo'svertical data shard partitioned horizontally across its clients. We proposeTiered Decentralized Coordinate Descent (TDCD), a communication-efficientdecentralized training algorithm for such two-tiered networks. To reducecommunication overhead, the clients in each silo perform multiple localgradient steps before sharing updates with their hub. Each hub adjusts itscoordinates by averaging its workers' updates, and then hubs exchangeintermediate updates with one another. We present a theoretical analysis of ouralgorithm and show the dependence of the convergence rate on the number ofvertical partitions, the number of local updates, and the number of clients ineach hub. We further validate our approach empirically via simulation-basedexperiments using a variety of datasets and both convex and non-convexobjectives.

Multi-Tier Federated Learning for Vertically Partitioned Data