Hierarchical policies are a key ingredient of intelligent behavior, expressing the different levels of abstraction involved in the solution of a problem. Learning hierarchical policies, however, remains a challenge, as no general learning principles have been identified for this purpose, despite the broad interest and vast literature in both model-free reinforcement learning and model-based planning. In this work, we introduce a principled method for learning hierarchical policies over classical planning domains, with no supervision from small instances. The method is based on learning to decompose problems into subproblems so that the subproblems have a lower complexity as measured by their width. Problems and subproblems are captured by means of sketch rules, and the scheme for reducing the width of sketch rules is applied iteratively until the final sketch rules have zero width and encode a general policy. We evaluate the learning method on a number of classical planning domains, analyze the resulting hierarchical policies, and prove their properties. We also show that learning hierarchical policies by learning and refining sketches iteratively is often more efficient than learning flat general policies in one shot.

Recently, sketches have been introduced as a general language for representing the subgoal structure of instances drawn from the same domain. Sketches are collections of rules of the form C -> E over a given set of features where C expresses Boolean conditions and E expresses qualitative changes. Each sketch rule defines a subproblem: going from a state that satisfies C to a state that achieves the change expressed by E or a goal state. Sketches can encode simple goal serializations, general policies, or decompositions of bounded width that can be solved greedily, in polynomial time, by the SIW_R variant of the SIW algorithm. Previous work has shown the computational value of sketches over benchmark domains that, while tractable, are challenging for domain-independent planners. In this work, we address the problem of learning sketches automatically given a planning domain, some instances of the target class of problems, and the desired bound on the sketch width. We present a logical formulation of the problem, an implementation using the ASP solver Clingo, and experimental results. The sketch learner and the SIW_R planner yield a domain-independent planner that learns and exploits domain structure in a crisp and explicit form.

Width-based planning methods deal with conjunctive goals by decomposing problems into subproblems of low width. Algorithms like SIW thus fail when the goal is not easily serializable in this way or when some of the subproblems have a high width. In this work, we address these limitations by using a simple but powerful language for expressing finer problem decompositions introduced recently by Bonet and Geffner, called policy sketches. A policy sketch R over a set of Boolean and numerical features is a set of sketch rules that express how the values of these features are supposed to change. Like general policies, policy sketches are domain general, but unlike policies, the changes captured by sketch rules do not need to be achieved in a single step. We show that many planning domains that cannot be solved by SIW are provably solvable in low polynomial time with the SIW_R algorithm, the version of SIW that employs user-provided policy sketches. Policy sketches are thus shown to be a powerful language for expressing domain-specific knowledge in a simple and compact way and a convenient alternative to languages such as HTNs or temporal logics. Furthermore, they make it easy to express general problem decompositions and prove key properties of them like their width and complexity.

Cost partitioning admissibly combines the information from multiple heuristics for optimal state-space search. One of the strongest cost partitioning algorithms is saturated cost partitioning. It considers the heuristics in sequence and assigns to each heuristic the minimal fraction of the remaining costs that are needed for preserving all heuristic estimates. Saturated cost partitioning has recently been generalized in two directions: first, by allowing to use different costs for the transitions induced by the same operator, and second, by preserving the heuristic estimates for only a subset of states. In this work, we unify these two generalizations and show that the resulting subset-saturated transition cost partitioning algorithm usually yields stronger heuristics than the two generalizations by themselves.