  Many machine learning models involve solving optimization problems. Thus, it
is important to deal with a large-scale optimization problem in big data
applications. Recently, subsampled Newton methods have emerged to attract much
attention due to their efficiency at each iteration, rectified a weakness in
the ordinary Newton method of suffering a high cost in each iteration while
commanding a high convergence rate. Other efficient stochastic second order
methods are also proposed. However, the convergence properties of these methods
are still not well understood. There are also several important gaps between
the current convergence theory and the performance in real applications. In
this paper, we aim to fill these gaps. We propose a unifying framework to
analyze both local and global convergence properties of second order methods.
Based on this framework, we present our theoretical results which match the
performance in real applications well.
