An Empirical Study of Perfect Potential Heuristics

Correlation complexity is a measure of a planning task indicating how hard it is. The introducing work, provides sufficient criteria to detect a correlation complexity of 2 on a planning task. It also introduced an example of a planning task with correlation complexity 3. In our work, we introduce a criterion to detect an arbitrary correlation complexity and extend the mentioned example to show with the new criterion that planning tasks with arbitrary correlation complexity exist.

Section: Gray Counter Taskmentioning

confidence: 99%

Higher-Dimensional Potential Heuristics: Lower Bound Criterion and Connection to Correlation Complexity

Dold,

Helmert

2024

“…I ∈ S fin (5) The final and most general variant follows the same idea as ∞DDA of "pruning" states with infinite heuristic value, but uses a second potential function to determine which states receive an infinite heuristic value. This was first suggested by Corrêa and Pommerening (2019) for the problem of representing the perfect heuristic h * as a potential function. They define heuristics h based on two potential functions h pot 1 and h pot 2 as follows:…”

Section: Dda Variants Without Aliveness Testsmentioning

confidence: 99%

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

Helmert

Sievers

Rovner³

et al. 2022

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.

“…Incrementally Extending the Set of Subproblems Corrêa and Pommerening (2019) show that encoding the optimal heuristic usually requires considering a large number of small projections but only a small number of larger projections. (They consider potential heuristics which partition costs over projection heuristics.)…”

Section: Restricting the Considered Patternsmentioning

confidence: 99%

Dantzig-Wolfe Decomposition for Cost Partitioning

Pommerening

Keller

Halasi³

et al. 2021

Self Cite

Optimal cost partitioning can produce high quality heuristic estimates even from small abstractions. It can be computed with a linear program (LP) but the size of this LP often makes this impractical. Recent work used Lagrangian decomposition to speed up the computation. Here we use a different decomposition technique called Dantzig-Wolfe decomposition to tackle the problem. This gives new insights into optimal cost partitioning and has several advantages over Lagrangian decomposition: our method detects when a cost partition is optimal; it can deal with general cost functions; and it does not consider abstractions in the linear program that do not contribute to the heuristic value. We also show the advantage of the method empirically and investigate several improvements that are useful for all cost partitioning methods.