Hierarchical Reinforcement Learning for Deep Goal Reasoning: An Expressiveness Analysis

Hierarchical DQN (h-DQN) is a two-level architecture of feedforward neural networks where the meta level selects goals and the lower level takes actions to achieve the goals. We show tasks that cannot be solved by h-DQN, exemplifying the limitation of this type of hierarchical framework (HF). We describe the recurrent hierarchical framework (RHF), generalizing architectures that use a recurrent neural network at the meta level. We analyze the expressiveness of HF and RHF using context-sensitive grammars. We show that RHF is more expressive than HF. We perform experiments comparing an implementation of RHF with two HF baselines; the results corroborate our theoretical findings.