  We reformulate the option framework as two parallel augmented MDPs. Under
this novel formulation, all policy optimization algorithms can be used off the
shelf to learn intra-option policies, option termination conditions, and a
master policy over options. We apply an actor-critic algorithm on each
augmented MDP, yielding the Double Actor-Critic (DAC) architecture.
Furthermore, we show that, when state-value functions are used as critics, one
critic can be expressed in terms of the other, and hence only one critic is
necessary. We conduct an empirical study on challenging robot simulation tasks.
In a transfer learning setting, DAC outperforms both its hierarchy-free
counterpart and previous gradient-based option learning algorithms.
