An Empirical Study of Perfect Potential Heuristics

Potential heuristics are weighted functions over state features of a planning task. A recent study defines the complexity of a task as the minimum required feature complexity for a potential heuristic that makes a search backtrack-free. This gives an indication of how complex potential heuristics need to be to achieve good results in satisficing planning. However, these results do not directly transfer to optimal planning. In this paper, we empirically study how complex potential heuristics must be to represent the perfect heuristic and how close to perfect heuristics can get with a limited number of features. We aim to identify the practical trade-offs between size, complexity and time for the quality of potential heuristics. Our results show that, even for simple planning tasks, finding perfect potential heuristics might be harder than expected

Best-First Width Search for Lifted Classical Planning

Lifted planners are useful to solve tasks that are too hard to ground. Still, computing informative lifted heuristics is difficult: directly adapting ground heuristics to the lifted setting is often too expensive, and extracting heuristics from the lifted representation can be uninformative. A natural alternative for lifted planners is to use width-based search. These algorithms are among the strongest for ground planning, even the variants that do not access the action model. In this work, we adapt best-first width search to the lifted setting and show that this yields state-of-the-art performance for hard-to-ground planning tasks

Mechanically Proving Guarantees of Generalized Heuristics: First Results and Ongoing Work

The goal of generalized planning is to find a solution that works for all tasks of a specific planning domain. Ideally, this solution is also efficient (i.e., polynomial) in all tasks. One possible approach is to learn such a solution from training examples and then prove that this generalizes for any given task. However, such proofs are usually pen-and-paper proofs written by a human. In our paper, we aim at automating these proofs so we can use a theorem prover to show that a solution generalizes for any task. Furthermore, we want to prove that this generalization works while still preserving efficiency. Our focus is on generalized potential heuristics encoding tiered measures of progress, which can be proven to lead to a find in a polynomial number of steps in all tasks of a domain. We show our ongoing work in this direction using the interactive theorem prover Isabelle/HOL. We illustrate the key aspects of our implementation using the Miconic domain and then discuss possible obstacles and challenges to fully automating this pipeline

On the Complexity of Heuristic Synthesis for Satisficing Classical Planning: Potential Heuristics and Beyond

Potential functions are a general class of heuristics for classical planning. For satisficing planning, previous work suggested the use of descending and dead-end avoiding (DDA) potential heuristics, which solve planning tasks by backtrack-free search. In this work we study the complexity of devising DDA potential heuristics for classical planning tasks. We show that verifying or synthesizing DDA potential heuristics is PSPACE-complete, but suitable modifications of the DDA properties reduce the complexity of these problems to the first and second level of the polynomial hierarchy. We also discuss the implications of our results for other forms of heuristic synthesis in classical planning

Lifted Successor Generation using Query Optimization Techniques

The standard PDDL language for classical planning uses sev eral first-order features, such as schematic actions. Yet, most classical planners ground this first-order representation into a propositional one as a preprocessing step. While this simpli fies the design of other parts of the planner, in several bench- marks the grounding process causes an exponential blowup that puts otherwise solvable tasks out of reach of the planners. In this work, we take a step towards planning with lifted representations . We tackle the successor generation task, a key operation in forward-search planning, directly on the lifted representation using well-known techniques from database theory . We show how computing the variable substitutions that make an action schema applicable in a given state is essentially a query evaluation problem. Interestingly, a large number of the action schemas in the standard benchmarks result in acyclic conjunctive queries, for which query evaluation is tractable. Our empirical results show that our approach is competitive with the standard (grounded) successor generation techniques in a few domains and outperforms them on benchmarks where grounding is challenging or infeasible

The FF Heuristic for Lifted Classical Planning

Heuristics for lifted planning are not yet as informed as the best heuristics for ground planning. Recent work introduced the idea of using Datalog programs to compute the additive heuristic over lifted tasks. Based on this work, we show how to compute the more informed FF heuristic in a lifted manner. We extend the Datalog program with executable annotations that can also be used to define other delete-relaxation heuristics. In our experiments, we show that a planner using the lifted FF implementation produces state-of-the-art results for lifted planners. It also reduces the gap to state-of-the-art ground planners in domains where grounding is feasible

Generalized Potential Heuristics for Classical Planning

Generalized planning aims at computing solutions that work for all instances of the same domain. In this paper, we show that several interesting planning domains possess compact generalized heuristics that can guide a greedy search in guaranteed polynomial time to the goal, and which work for any instance of the domain . These heuristics are weighted sums of state features that capture the number of objects satisfying a certain first-order logic property in any given state. These features have a meaningful interpretation and generalize naturally to the whole domain. Additionally, we present an approach based on mixed integer linear programming to compute such heuristics automatically from the observation of small training instances. We develop two variations of the approach that progressively refine the heuristic as new states are encountered. We illustrate the approach empirically on a number of standard domains, where we show that the generated heuristics will correctly generalize to all possible instances

Machetli: Simplifying Input Files for Debugging

Debugging can be a painful task, especially when bugs only occur for large input files. We present Machetli, a tool to help with debugging in such situations. It takes a large input file and cuts away parts of it, while still provoking the bug. The resulting file is much smaller than the original, making the bug easier to find and fix. In our experience, Machetli was able to reduce planning tasks with thousands of actions to trivial tasks that could even be solved by hand. Machetli is an open-source project and it can be extended to other use cases such as debugging SAT solvers or LaTeX compilation bugs

Relaxed Decision Diagrams for Delete-Free Planning

In this work, we investigate the computation of optimal plans for delete-free tasks using relaxed decision diagrams. We introduce a new method to compute approximations of h+ in polynomial time on the width of the RDD and show that this approximation is a lower bound for the optimal solution. We analyze different strategies to construct decision diagrams and compare these approximations to h+