  This work proposes a distributed algorithm for solving empirical risk
minimization problems, called L-DQN, under the master/worker communication
model. L-DQN is a distributed limited-memory quasi-Newton method that supports
asynchronous computations among the worker nodes. Our method is efficient both
in terms of storage and communication costs, i.e., in every iteration the
master node and workers communicate vectors of size $O(d)$, where $d$ is the
dimension of the decision variable, and the amount of memory required on each
node is $O(md)$, where $m$ is an adjustable parameter. To our knowledge, this
is the first distributed quasi-Newton method with provable global linear
convergence guarantees in the asynchronous setting where delays between nodes
are present. Numerical experiments are provided to illustrate the theory and
the practical performance of our method.
