DAGC: Data-Volume-Aware Adaptive Sparsification Gradient Compression for Distributed Machine Learning in Mobile Computing

Distributed machine learning (DML) in mobile environments faces significant communication bottlenecks. Gradient compression has emerged as an effective solution to this issue, offering substantial benefits in environments with limited bandwidth and metered data. Yet, they encounter severe performance drop in non-IID environments due to a one-size-fits-all compression approach, which does not account for the varying data volumes across workers. Assigning varying compression ratios to workers with distinct data distributions and volumes is thus a promising solution. This study introduces an analysis of distributed SGD with non-uniform compression, which reveals that the convergence rate (indicative of the iterations needed to achieve a certain accuracy) is influenced by compression ratios applied to workers with differing volumes. Accordingly, we frame relative compression ratio assignment as an $n$-variables chi-square nonlinear optimization problem, constrained by a fixed and limited communication budget. We propose DAGC-R, which assigns the worker handling larger data volumes the conservative compression. Recognizing the computational limitations of mobile devices, we DAGC-A, which are computationally less demanding and enhances the robustness of the absolute gradient compressor in non-IID scenarios. Our experiments confirm that both the DAGC-A and DAGC-R can achieve better performance when dealing with highly imbalanced data volume distribution and restricted communication.