  Distributed machine learning (DML) over time-varying networks can be an
enabler for emerging decentralized ML applications such as autonomous driving
and drone fleeting. However, the commonly used weighted arithmetic mean model
aggregation function in existing DML systems can result in high model loss, low
model accuracy, and slow convergence speed over time-varying networks. To
address this issue, in this paper, we propose a novel non-linear class of model
aggregation functions to achieve efficient DML over time-varying networks.
Instead of taking a linear aggregation of neighboring models as most existing
studies do, our mechanism uses a nonlinear aggregation, a weighted power-p mean
(WPM), as the aggregation function of local models from neighbors. The
subsequent optimizing steps are taken using mirror descent defined by a Bregman
divergence that maintains convergence to optimality. In this paper, we analyze
properties of the WPM and rigorously prove convergence properties of our
aggregation mechanism. Additionally, through extensive experiments, we show
that when p > 1, our design significantly improves the convergence speed of the
model and the scalability of DML under time-varying networks compared with
arithmetic mean aggregation functions, with little additional computation
overhead.
