  We study distributed algorithms for expected loss minimization where the
datasets are large and have to be stored on different machines. Often we deal
with minimizing the average of a set of convex functions where each function is
the empirical risk of the corresponding part of the data. In the distributed
setting where the individual data instances can be accessed only on the local
machines, there would be a series of rounds of local computations followed by
some communication among the machines. Since the cost of the communication is
usually higher than the local machine computations, it is important to reduce
it as much as possible. However, we should not allow this to make the
computation too expensive to become a burden in practice. Using second-order
methods could make the algorithms converge faster and decrease the amount of
communication needed. There are some successful attempts in developing
distributed second-order methods. Although these methods have shown fast
convergence, their local computation is expensive and could enjoy more
improvement for practical uses. In this study we modify an existing approach,
DANE (Distributed Approximate NEwton), in order to improve the computational
cost while maintaining the accuracy. We tackle this problem by using iterative
methods for solving the local subproblems approximately instead of providing
exact solutions for each round of communication. We study how using different
iterative methods affect the behavior of the algorithm and try to provide an
appropriate tradeoff between the amount of local computation and the required
amount of communication. We demonstrate the practicality of our algorithm and
compare it to the existing distributed gradient based methods such as SGD.
