Incremental Search for Counterexample-Guided Cartesian Abstraction Refinement

Counterexample-guided Cartesian abstraction refinement has been shown to yield informative heuristics for optimal classical planning. The algorithm iteratively finds an abstract solution and uses it to decide how to refine the abstraction. Since the abstraction grows in each step, finding solutions is the main bottleneck of the refinement loop. We cast the refinements as an incremental search problem and show that this drastically reduces the time for computing abstractions

Online Saturated Cost Partitioning for Classical Planning

Saturated cost partitioning is a general method for admissiblyadding heuristic estimates for optimal state-space search. Thealgorithm strongly depends on the order in which it considers the heuristics. The strongest previous approach precomputes a set of diverse orders and the corresponding saturatedcost partitionings before the search. This makes evaluatingthe overall heuristic very fast, but requires a long precomputation phase. By diversifying the set of orders online duringthe search we drastically speed up the planning process andeven solve slightly more tasks

Adaptive search techniques in AI planning and heuristic search

State-space search is a common approach to solve problems appearing in artificial intelligence and other subfields of computer science. In such problems, an agent must find a sequence of actions leading from an initial state to a goal state. However, the state spaces of practical applications are often too large to explore exhaustively. Hence, heuristic functions that estimate the distance to a goal state (such as straight-line distance for navigation tasks) are used to guide the search more effectively. Heuristic search is typically viewed as a static process. The heuristic function is assumed to be unchanged throughout the search, and its resulting values are directly used for guidance without applying any further reasoning to them. Yet critical aspects of the task may only be discovered during the search, e.g., regions of the state space where the heuristic does not yield reliable values. Our work here aims to make this process more dynamic, allowing the search to adapt to such observations. One form of adaptation that we consider is online refinement of the heuristic function. We design search algorithms that detect weaknesses in the heuristic, and address them with targeted refinement operations. If the heuristic converges to perfect estimates, this results in a secondary method of progress, causing search algorithms that are otherwise incomplete to eventually find a solution. We also consider settings that inherently require adaptation: In online replanning, a plan that is being executed must be amended for changes in the environment. Similarly, in real-time search, an agent must act under strict time constraints with limited information. The search algorithms we introduce in this work share a common pattern of online adaptation, allowing them to effectively react to challenges encountered during the search. We evaluate our contributions on a wide range of standard benchmarks. Our results show that the flexibility of these algorithms makes them more robust than traditional approaches, and they often yield substantial improvements over current state-of-the-art planners.Die Zustandsraumsuche ist ein oft verwendeter Ansatz um verschiedene Probleme zu lösen, die in der Künstlichen Intelligenz und anderen Bereichen der Informatik auftreten. Dabei muss ein Akteur eine Folge von Aktionen finden, die einen Pfad von einem Startzustand zu einem Zielzustand bilden. Die Zustandsräume von praktischen Anwendungen sind häufig zu groß um sie vollständig zu durchsuchen. Aus diesem Grund leitet man die Suche mit Heuristiken, die die Distanz zu einem Zielzustand abschätzen; zum Beispiel lässt sich die Luftliniendistanz als Heuristik für Navigationsprobleme einsetzen. Heuristische Suche wird typischerweise als statischer Prozess angesehen. Man nimmt an, dass die Heuristik während der Suche eine unveränderte Funktion ist, und die resultierenden Werte werden direkt zur Leitung der Suche benutzt ohne weitere Logik darauf anzuwenden. Jedoch könnten kritische Aspekte des Problems erst im Laufe der Suche erkannt werden, wie zum Beispiel Bereiche des Zustandsraums in denen die Heuristik keine verlässlichen Abschätzungen liefert. In dieser Arbeit wird der Suchprozess dynamischer gestaltet und der Suche ermöglicht sich solchen Beobachtungen anzupassen. Eine Art dieser Anpassung ist die Onlineverbesserung der Heuristik. Es werden Suchalgorithmen entwickelt, die Schwächen in der Heuristik erkennen und mit gezielten Verbesserungsoperationen beheben. Wenn die Heuristik zu perfekten Werten konvergiert ergibt sich daraus eine zusätzliche Form von Fortschritt, wodurch auch Suchalgorithmen, die sonst unvollständig sind, garantiert irgendwann eine Lösung finden werden. Es werden auch Szenarien betrachtet, die schon von sich aus Anpassung erfordern: In der Onlineumplanung muss ein Plan, der gerade ausgeführt wird, auf Änderungen in der Umgebung angepasst werden. Ähnlich dazu muss sich ein Akteur in der Echtzeitsuche unter strengen Zeitauflagen und mit eingeschränkten Informationen bewegen. Die Suchalgorithmen, die in dieser Arbeit eingeführt werden, folgen einem gemeinsamen Muster von Onlineanpassung, was ihnen ermöglicht effektiv auf Herausforderungen zu reagieren die im Verlauf der Suche aufkommen. Diese Ansätze werden auf einer breiten Reihe von Benchmarks ausgewertet. Die Ergebnisse zeigen, dass die Flexibilität dieser Algorithmen zu erhöhter Zuverlässigkeit im Vergleich zu traditionellen Ansätzen führt, und es werden oft deutliche Verbesserungen gegenüber modernen Planungssystemen erzielt.DFG grant 389792660 as part of TRR 248 – CPEC (see https://perspicuous-computing.science), and DFG grant HO 2169/5-1, "Critically Constrained Planning via Partial Delete Relaxation

Counterexample-Guided Cartesian Abstraction Refinement for Classical Planning

Counterexample-guided abstraction refinement (CEGAR) is a method for incrementally computing abstractions of transition systems. We propose a CEGAR algorithm for computing abstraction heuristics for optimal classical planning. Starting from a coarse abstraction of the planning task, we iteratively compute an optimal abstract solution, check if and why it fails for the concrete planning task and refine the abstraction so that the same failure cannot occur in future iterations. A key ingredient of our approach is a novel class of abstractions for classical planning tasks that admits efficient and very fine-grained refinement. Since a single abstraction usually cannot capture enough details of the planning task, we also introduce two methods for producing diverse sets of heuristics within this framework, one based on goal atoms, the other based on landmarks. In order to sum their heuristic estimates admissibly we introduce a new cost partitioning algorithm called saturated cost partitioning. We show that the resulting heuristics outperform other state-of-the-art abstraction heuristics in many benchmark domains

Counterexample-guided cartesian abstraction refinement and saturated cost partitioning for optimal classical planning

Heuristic search with an admissible heuristic is one of the most prominent approaches to solving classical planning tasks optimally. In the first part of this thesis, we introduce a new family of admissible heuristics for classical planning, based on Cartesian abstractions, which we derive by counterexample-guided abstraction refinement. Since one abstraction usually is not informative enough for challenging planning tasks, we present several ways of creating diverse abstractions. To combine them admissibly, we introduce a new cost partitioning algorithm, which we call saturated cost partitioning. It considers the heuristics sequentially and uses the minimum amount of costs that preserves all heuristic estimates for the current heuristic before passing the remaining costs to subsequent heuristics until all heuristics have been served this way. In the second part, we show that saturated cost partitioning is strongly influenced by the order in which it considers the heuristics. To find good orders, we present a greedy algorithm for creating an initial order and a hill-climbing search for optimizing a given order. Both algorithms make the resulting heuristics significantly more accurate. However, we obtain the strongest heuristics by maximizing over saturated cost partitioning heuristics computed for multiple orders, especially if we actively search for diverse orders. The third part provides a theoretical and experimental comparison of saturated cost partitioning and other cost partitioning algorithms. Theoretically, we show that saturated cost partitioning dominates greedy zero-one cost partitioning. The difference between the two algorithms is that saturated cost partitioning opportunistically reuses unconsumed costs for subsequent heuristics. By applying this idea to uniform cost partitioning we obtain an opportunistic variant that dominates the original. We also prove that the maximum over suitable greedy zero-one cost partitioning heuristics dominates the canonical heuristic and show several non-dominance results for cost partitioning algorithms. The experimental analysis shows that saturated cost partitioning is the cost partitioning algorithm of choice in all evaluated settings and it even outperforms the previous state of the art in optimal classical planning

Saturated Post-hoc Optimization for Classical Planning

Saturated cost partitioning and post-hoc optimization are two powerful cost partitioning algorithms for optimal classical planning. The main idea of saturated cost partitioning is to give each considered heuristic only the fraction of remaining operator costs that it needs to prove its estimates. We show how to apply this idea to post-hoc optimization and obtain a heuristic that dominates the original both in theory and on the IPC benchmarks

Subset-Saturated Cost Partitioning for Optimal Classical Planning

Cost partitioning is a method for admissibly adding multiple heuristics for state-space search. Saturated cost partitioning considers the given heuristics in sequence, assigning to each heuristic the minimum fraction of remaining costs that it needs to preserve its estimates for all states. We generalize saturated cost partitioning by allowing to preserve the heuristic values of only a subset of states and show that this often leads to stronger heuristics