The Eigenoption-Critic Framework
  Eigenoptions (EOs) have been recently introduced as a promising idea for
generating a diverse set of options through the graph Laplacian, having been
shown to allow efficient exploration. Despite its initial promising results, a
couple of issues in current algorithms limit its application, namely: (1) EO
methods require two separate steps (eigenoption discovery and reward
maximization) to learn a control policy, which can incur a significant amount
of storage and computation; (2) EOs are only defined for problems with discrete
state-spaces and; (3) it is not easy to take the environment's reward function
into consideration when discovering EOs. To addresses these issues, we
introduce an algorithm termed eigenoption-critic (EOC) based on the
Option-critic (OC) framework [Bacon17], a general hierarchical reinforcement
learning (RL) algorithm that allows learning the intra-option policies
simultaneously with the policy over options. We also propose a generalization
of EOC to problems with continuous state-spaces through the Nystr\"om
approximation. EOC can also be seen as extending OC to nonstationary settings,
where the discovered options are not tailored for a single task.
