Hierarchical Solution of Markov Decision Processes using Macro-actions (1301.7381v1)

Abstract: We investigate the use of temporally abstract actions, or macro-actions, in the solution of Markov decision processes. Unlike current models that combine both primitive actions and macro-actions and leave the state space unchanged, we propose a hierarchical model (using an abstract MDP) that works with macro-actions only, and that significantly reduces the size of the state space. This is achieved by treating macroactions as local policies that act in certain regions of state space, and by restricting states in the abstract MDP to those at the boundaries of regions. The abstract MDP approximates the original and can be solved more efficiently. We discuss several ways in which macro-actions can be generated to ensure good solution quality. Finally, we consider ways in which macro-actions can be reused to solve multiple, related MDPs; and we show that this can justify the computational overhead of macro-action generation.

• The paper introduces an abstract MDP model that uses macro-actions to reduce state-space size by focusing on boundary states.
• The paper presents strategies for generating and reusing macro-actions to optimize computational efficiency within related MDPs.
• The paper demonstrates through experiments that the hierarchical approach outperforms augmented MDPs in convergence time and overall efficiency.

Hierarchical Solution of Markov Decision Processes using Macro-actions

The paper "Hierarchical Solution of Markov Decision Processes using Macro-actions" investigates an alternative approach to handling large state and action spaces within Markov Decision Processes (MDPs) by introducing a hierarchical model based on macro-actions. This work diverges from previous methods that maintained unchanged state spaces and incorporated both primitive actions and macro-actions.

Key Contributions

1. Introduction of an Abstract MDP: The authors propose an abstract model, which significantly reduces the size of the MDP state space by incorporating macro-actions as local policies that manage specific regions. This model focuses solely on macro-actions, treating states at the boundaries of these regions, allowing for the original MDP to be approximated and solved more efficiently.
2. Macro-action Generation and Reuse: The paper details multiple strategies to generate macro-actions that ensure high solution quality and discusses the feasibility of reusing these macro-actions to solve multiple related MDPs. This reuse justifies the computational overhead associated with macro-action generation.
3. Hierarchical Model Implementation: Through experimentation, the authors provide evidence that their hierarchical approach indeed offers computational savings. They utilize a partitioning of state space into regions, generating local policies (macros) for each region, which are then used in a simplified abstract MDP that only considers the peripheral states of these regions.
4. Advantages over Augmented MDPs: Unlike augmented MDPs where macros do not necessarily reduce computation time, the hierarchical MDP's reduction in state space size and the strategic use of macros for decision-making at peripheral states offer a more efficient solution pathway.

Experimental Verification

In experimental settings, the authors demonstrate the computational efficiency and potential solution quality of their hierarchical model using a simple navigation problem in a maze environment. By conducting value iteration on both augmented MDPs and abstract MDPs, the results showcase the benefits in convergence time when employing macro-actions. Interestingly, they point out certain drawbacks, such as slower convergence in augmented MDPs when poor initial values are employed, contrasted against the abstract MDP approach which yielded near-optimal solutions quickly.

Implications and Future Directions

The hierarchical solution framework proposed herein has significant practical implications for AI systems facing dynamic or repeated problem-solving tasks. By pre-computing a set of macros based on anticipated variations in task or environment, AI systems can achieve swift, on-line responses to evolving scenarios. The concept of hybrid MDPs, wherein both abstract and base levels are dynamically employed based on changes within specific regions, further extends the model's utility by balancing computational load and solution effectiveness.

Looking forward, this approach encourages further research on optimal state space decomposition strategies, efficient macro model representation, and real-time dynamic adjustment of macros based on ongoing assessments of MDP alterations. Moreover, tackling computational costs of macro generation through approximation methods could enhance the feasibility of widespread adoption of this methodology in large-scale AI applications.

In conclusion, this paper provides a methodologically sound framework that not only addresses the inherent complexity challenges within MDPs but also paves the way for practical, scalable AI systems capable of rapid adaptation to diverse problem instances.