Title: Cross-Silo Federated Learning for Multi-Tier Networks with Vertical and Horizontal Data Partitioning

Abstract: We consider federated learning in tiered communication networks. Our network model consists of a set of silos, each holding a vertical partition of the data. Each silo contains a hub and a set of clients, with the silo's vertical data shard partitioned horizontally across its clients. We propose Tiered Decentralized Coordinate Descent (TDCD), a communication-efficient decentralized training algorithm for such two-tiered networks. The clients in each silo perform multiple local gradient steps before sharing updates with their hub to reduce communication overhead. Each hub adjusts its coordinates by averaging its workers' updates, and then hubs exchange intermediate updates with one another. We present a theoretical analysis of our algorithm and show the dependence of the convergence rate on the number of vertical partitions and the number of local updates. We further validate our approach empirically via simulation-based experiments using a variety of datasets and objectives.