  Goal-conditioned hierarchical reinforcement learning (HRL) is a promising
approach for scaling up reinforcement learning (RL) techniques. However, it
often suffers from training inefficiency as the action space of the high-level,
i.e., the goal space, is often large. Searching in a large goal space poses
difficulties for both high-level subgoal generation and low-level policy
learning. In this paper, we show that this problem can be effectively
alleviated by restricting the high-level action space from the whole goal space
to a $k$-step adjacent region of the current state using an adjacency
constraint. We theoretically prove that the proposed adjacency constraint
preserves the optimal hierarchical policy in deterministic MDPs, and show that
this constraint can be practically implemented by training an adjacency network
that can discriminate between adjacent and non-adjacent subgoals. Experimental
results on discrete and continuous control tasks show that incorporating the
adjacency constraint improves the performance of state-of-the-art HRL
approaches in both deterministic and stochastic environments.
