  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.
