  Though quasi-Newton methods have been extensively studied in the literature,
they either suffer from local convergence or use a series of line searches for
global convergence which is not acceptable in the distributed setting. In this
work, we first propose a line search free greedy quasi-Newton (GQN) method with
adaptive steps and establish explicit non-asymptotic bounds for both the global
convergence rate and local superlinear rate. Our novel idea lies in the design
of multiple greedy quasi-Newton updates, which involves computing
Hessian-vector products, to control the Hessian approximation error, and a
simple mechanism to adjust stepsizes to ensure the objective function
improvement per iterate. Then, we extend it to the master-worker framework and
propose a distributed adaptive GQN method whose communication cost is
comparable with that of first-order methods, yet it retains the superb
convergence property of its centralized counterpart. Finally, we demonstrate
the advantages of our methods via numerical experiments.
