  Due to the big size of data and limited data storage volume of a single
computer or a single server, data are often stored in a distributed manner.
Thus, performing large-scale machine learning operations with the distributed
datasets through communication networks is often required. In this paper, we
study the convergence rate of the distributed dual coordinate ascent for
distributed machine learning problems in a general tree-structured network.
Since a tree network model can be understood as the generalization of a star
network model, our algorithm can be thought of as the generalization of the
distributed dual coordinate ascent in a star network model. We provide the
convergence rate of the distributed dual coordinate ascent over a general tree
network in a recursive manner and analyze the network effect on the convergence
rate. Secondly, by considering network communication delays, we optimize the
distributed dual coordinate ascent algorithm to maximize its convergence speed.
From our analytical result, we can choose the optimal number of local
iterations depending on the communication delay severity to achieve the fastest
convergence speed. In numerical experiments, we consider machine learning
scenarios over communication networks, where local workers cannot directly
reach to a central node due to constraints in communication, and demonstrate
that the usability of our distributed dual coordinate ascent algorithm in tree
networks. Additionally, we show that adapting number of local and global
iterations to network communication delays in the distributed dual coordinated
ascent algorithm can improve its convergence speed.
