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. Our experiments on challenging robot simulation tasks demonstrate that DAC outperforms previous gradient-based option learning algorithms by a large margin and significantly outperforms its hierarchy-free counterparts in a transfer learning setting.
Many components in @math are not new. The idea of an augmented MDP is suggested by @cite_9 in AHP. The augmented state spaces @math and @math are also used by @cite_2 to simplify the derivation. Applying vanilla policy gradient to @math and @math leads immediately to the Intra-Option Policy Gradient Theorem . The augmented policy @math is also used by @cite_10 to simplify the derivation. However, neither OC nor IOPG works on the augmented state space directly. To the best of our knowledge, @math is the first time that the two augmented MDPs are formulated explicitly. It is this explicit formulation that allows the off-the-shelf application of all state-of-the-art policy optimizations algorithm and combines advantages from both OC and AHP, yielding a significant empirical performance boost. Furthermore, it is this explicit formulation that generates a family of policy-based intra-option algorithms for master policy learning.
@cite_9 @cite_10 @cite_2
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Temporally extended actions (or macro-actions) have proven useful for speeding up planning and learning, adding robustness, and building prior knowledge into AI systems. The options framework, as introduced in Sutton, Precup and Singh (1999), provides a natural way to incorporate macro-actions into reinforcement learning. In the subgoals approach, learning is divided into two phases, first learning each option with a prescribed subgoal, and then learning to compose the learned options together. In this paper we offer a unified framework for concurrent inter- and intra-options learning. To that end, we propose a modular parameterization of intra-option policies together with option termination conditions and the option selection policy (inter options), and show that these three decision components may be viewed as a unified policy over an augmented state-action space, to which standard policy gradient algorithms may be applied. We identify the basis functions that apply to each of these decision components, and show that they possess a useful orthogonality property that allows to compute the natural gradient independently for each component. We further outline the extension of the suggested framework to several levels of options hierarchy, and conclude with a brief illustrative example. In the pursuit of increasingly intelligent learning systems, abstraction plays a vital role in enabling sophisticated decisions to be made in complex environments. The options framework provides formalism for such abstraction over sequences of decisions. However most models require that options be given a priori, presumably specified by hand, which is neither efficient, nor scalable. Indeed, it is preferable to learn options directly from interaction with the environment. Despite several efforts, this remains a difficult problem: many approaches require access to a model of the environmental dynamics, and inferred options are often not interpretable, which limits our ability to explain the system behavior for verification or debugging purposes. In this work we develop a novel policy gradient method for the automatic learning of policies with options. This algorithm uses inference methods to simultaneously improve all of the options available to an agent, and thus can be employed in an off-policy manner, without observing option labels. Experimental results show that the options learned can be interpreted. Further, we find that the method presented here is more sample efficient than existing methods, leading to faster and more stable learning of policies with options. Temporal abstraction is key to scaling up learning and planning in reinforcement learning. While planning with temporally extended actions is well understood, creating such abstractions autonomously from data has remained challenging. We tackle this problem in the framework of options [Sutton, Precup & Singh, 1999; Precup, 2000]. We derive policy gradient theorems for options and propose a new option-critic architecture capable of learning both the internal policies and the termination conditions of options, in tandem with the policy over options, and without the need to provide any additional rewards or subgoals. Experimental results in both discrete and continuous environments showcase the flexibility and efficiency of the framework.