A Matrix Splitting Perspective on Planning with Options
  We show that the Bellman operator underlying the options framework leads to a
matrix splitting, an approach traditionally used to speed up convergence of
iterative solvers for large linear systems of equations. Based on standard
comparison theorems for matrix splittings, we then show how the asymptotic rate
of convergence varies as a function of the inherent timescales of the options.
This new perspective highlights a trade-off between asymptotic performance and
the cost of computation associated with building a good set of options.
