  In this paper, we consider distributed algorithms for solving the empirical
risk minimization problem under the master/worker communication model. We
develop a distributed asynchronous quasi-Newton algorithm that can achieve
superlinear convergence. To our knowledge, this is the first distributed
asynchronous algorithm with superlinear convergence guarantees. Our algorithm
is communication-efficient in the sense that at every iteration the master node
and workers communicate vectors of size $O(p)$, where $p$ is the dimension of
the decision variable. The proposed method is based on a distributed
asynchronous averaging scheme of decision vectors and gradients in a way to
effectively capture the local Hessian information of the objective function.
Our convergence theory supports asynchronous computations subject to both
bounded delays and unbounded delays with a bounded time-average. Unlike in the
majority of asynchronous optimization literature, we do not require choosing
smaller stepsize when delays are huge. We provide numerical experiments that
match our theoretical results and showcase significant improvement comparing to
state-of-the-art distributed algorithms.
