We study the problem of representation learning in goal-conditioned hierarchical reinforcement learning. In such hierarchical structures, a higher-level controller solves tasks by iteratively communicating goals which a lower-level policy is trained to reach. Accordingly, the choice of representation -- the mapping of observation space to goal space -- is crucial. To study this problem, we develop a notion of sub-optimality of a representation, defined in terms of expected reward of the optimal hierarchical policy using this representation. We derive expressions which bound the sub-optimality and show how these expressions can be translated to representation learning objectives which may be optimized in practice. Results on a number of difficult continuous-control tasks show that our approach to representation learning yields qualitatively better representations as well as quantitatively better hierarchical policies, compared to existing methods.
We translate a bound on sub-optimality of representations to a practical training objective in the context of hierarchical reinforcement learning. The authors proposes a novel approach in learning a representation for HRL and state an intriguing connection between representation learning and bounding the sub-optimality which results in a gradient based algorithm This paper proposes a way to handle sub-optimality in the context of learning representations which refer to the sub-optimality of hierarchical polity with respect to the task reward.