  Temporal abstraction refers to the ability of an agent to use behaviours of
controllers which act for a limited, variable amount of time. The options
framework describes such behaviours as consisting of a subset of states in
which they can initiate, an internal policy and a stochastic termination
condition. However, much of the subsequent work on option discovery has ignored
the initiation set, because of difficulty in learning it from data. We provide
a generalization of initiation sets suitable for general function
approximation, by defining an interest function associated with an option. We
derive a gradient-based learning algorithm for interest functions, leading to a
new interest-option-critic architecture. We investigate how interest functions
can be leveraged to learn interpretable and reusable temporal abstractions. We
demonstrate the efficacy of the proposed approach through quantitative and
qualitative results, in both discrete and continuous environments.
