We present three new complexity results for classes of planning problems with simple causal graphs. First, we describe a polynomial-time algorithm that uses macros to generate plans for the class 3S of planning problems with binary state variables and acyclic causal graphs. This implies that plan generation may be tractable even when a planning problem has an exponentially long minimal solution. We also prove that the problem of plan existence for planning problems with multi-valued variables and chain causal graphs is NP-hard. Finally, we show that plan existence for planning problems with binary state variables and polytree causal graphs is NP-complete.

Learning a complex task can be significantly facilitated by defining a hierarchy of subtasks. An agent can learn to choose between various temporally abstract actions, each solving an assigned subtask, to accomplish the overall task. In this paper, we study hierarchical learning using the framework of options. We argue that to take full advantage of hierarchical structure, one should perform option-specific state abstraction, and that if this is to scale to larger tasks, state abstraction should be automated. We adapt McCallum's U-Tree algorithm to automatically build option-specific representations of the state feature space, and we illustrate the resulting algorithm using a simple hierarchical task. Results suggest that automated option-specific state abstraction is an attractive approach to making hierarchical learning systems more effective.

Learning a complex task can be significantly facilitated by defining a hierarchy of subtasks. An agent can learn to choose between various temporally abstract actions, each solving an assigned subtask, to accomplish theoverall task. In this paper, we study hierarchical learning using the framework of options. We argue that to take full advantage of hierarchical structure,one should perform option-specific state abstraction, and that if this is to scale to larger tasks, state abstraction should be automated. Weadapt McCallum's U-Tree algorithm to automatically build option-specific representations of the state feature space, and we illustrate theresulting algorithm using a simple hierarchical task. Results suggest that automated option-specific state abstraction is an attractive approach to making hierarchical learning systems more effective.