  It is well known that options can make planning more efficient, among their
many benefits. Thus far, algorithms for autonomously discovering a set of
useful options were heuristic. Naturally, a principled way of finding a set of
useful options may be more promising and insightful. In this paper we suggest a
mathematical characterization of good sets of options using tools from
information theory. This characterization enables us to find conditions for a
set of options to be optimal and an algorithm that outputs a useful set of
options and illustrate the proposed algorithm in simulation.
