  This paper proposes a communication strategy for decentralized learning on
wireless systems. Our discussion is based on the decentralized parallel
stochastic gradient descent (D-PSGD), which is one of the state-of-the-art
algorithms for decentralized learning. The main contribution of this paper is
to raise a novel open question for decentralized learning on wireless systems:
there is a possibility that the density of a network topology significantly
influences the runtime performance of D-PSGD. In general, it is difficult to
guarantee delay-free communications without any communication deterioration in
real wireless network systems because of path loss and multi-path fading. These
factors significantly degrade the runtime performance of D-PSGD. To alleviate
such problems, we first analyze the runtime performance of D-PSGD by
considering real wireless systems. This analysis yields the key insights that
dense network topology (1) does not significantly gain the training accuracy of
D-PSGD compared to sparse one, and (2) strongly degrades the runtime
performance because this setting generally requires to utilize a low-rate
transmission. Based on these findings, we propose a novel communication
strategy, in which each node estimates optimal transmission rates such that
communication time during the D-PSGD optimization is minimized under the
constraint of network density, which is characterized by radio propagation
property. The proposed strategy enables to improve the runtime performance of
D-PSGD in wireless systems. Numerical simulations reveal that the proposed
strategy is capable of enhancing the runtime performance of D-PSGD.
