Enabling Communication-Efficient Federated Learning via Distributed Compressed Sensing

Federated learning (FL) trains a shared global model by periodically aggregating gradients from local devices. Communication overhead becomes a principal bottleneck in FL since participating devices usually suffer from limited bandwidth and unreliable connections in uplink transmission. To address this problem, the gradient compression methods based on compressed sensing (CS) theory have been put forward recently. However, most existing CS-based works compress gradients independently, ignoring the gradient correlations between participants or adjacent communication rounds, which constrains the achievement of higher compression rates. In view of the above observation, we propose a novel gradient compression scheme named FedDCS, guided by distributed compressed sensing (DCS) theory. Following the design philosophy of separate encoding and joint decoding in DCS, FedDCS compresses gradients for participants in each round separately while reconstructing them at the central server jointly via fully exploiting correlated gradients from the previous round, which are known as side information (SI). Benefiting from this design, reconstruction performance is significantly improved with fewer decoding errors also iterations under the identical compression rate, and the total uploading bits to achieve model convergence are considerably reduced. Theoretical analysis and extensive experiments conducted on MNIST and Fashion-MNIST both verify the effectiveness of our approach.