The options framework is a popular approach for building temporally extended actions in reinforcement learning. In particular, the option-critic architecture provides general purpose policy gradient theorems for learning actions from scratch that are extended in time. However, past work makes the key assumption that each of the components of option-critic has independent parameters. In this work we note that while this key assumption of the policy gradient theorems of option-critic holds in the tabular case, it is always violated in practice for the deep function approximation setting. We thus reconsider this assumption and consider more general extensions of option-critic and hierarchical option-critic training that optimize for the full architecture with each update. It turns out that not assuming parameter independence challenges a belief in prior work that training the policy over options can be disentangled from the dynamics of the underlying options. In fact, learning can be sped up by focusing the policy over options on states where options are actually likely to terminate. We put our new algorithms to the test in application to sample efficient learning of Atari games, and demonstrate significantly improved stability and faster convergence when learning long options.

Option-critic learning is a general-purpose reinforcement learning (RL) framework that aims to address the issue of long term credit assignment by leveraging temporal abstractions. However, when dealing with extended timescales, discounting future rewards can lead to incorrect credit assignments. In this work, we address this issue by extending the hierarchical option-critic policy gradient theorem for the average reward criterion. Our proposed framework aims to maximize the long-term reward obtained in the steady-state of the Markov chain defined by the agent's policy. Furthermore, we use an ordinary differential equation based approach for our convergence analysis and prove that the parameters of the intra-option policies, termination functions, and value functions, converge to their corresponding optimal values, with probability one. Finally, we illustrate the competitive advantage of learning options, in the average reward setting, on a grid-world environment with sparse rewards.