Incremental Lower Bounds for Additive Cost Planning Problems

We present a novel method for computing increasing lower bounds on the cost of solving planning problems, based on repeatedly solving and strengthening the delete relaxation of the problem. Strengthening is done by compiling select conjunctions into new atoms, similar to the P*m construction. Because it does not rely on search in the state space, this method does not suffer some of the weaknesses of admissible search algorithms and therefore is able to prove higher lower bounds for many problems that are too hard for optimal planners to solve, thus narrowing the gap between lower bound and cost of the best known plan, providing better assurances of plan quality

Capturing (Optimal) Relaxed Plans with Stable and Supported Models of Logic Programs

We establish a novel relation between delete-free planning, an important task for the AI Planning community also known as relaxed planning, and logic programming. We show that given a planning problem, all subsets of actions that could be ordered to produce relaxed plans for the problem can be bijectively captured with stable models of a logic program describing the corresponding relaxed planning problem. We also consider the supported model semantics of logic programs, and introduce one causal and one diagnostic encoding of the relaxed planning problem as logic programs, both capturing relaxed plans with their supported models. Our experimental results show that these new encodings can provide major performance gain when computing optimal relaxed plans, with our diagnostic encoding outperforming state-of-the-art approaches to relaxed planning regardless of the given time limit when measured on a wide collection of STRIPS planning benchmarks.Comment: Paper presented at the 39th International Conference on Logic Programming (ICLP 2023), 14 page

Improving delete relaxation heuristics through explicitly represented conjunctions

Heuristic functions based on the delete relaxation compute upper and lower bounds on the optimal delete-relaxation heuristic h+, and are of paramount importance in both optimal and satisficing planning. Here we introduce a principled and flexible technique for improving h+, by augmenting delete-relaxed planning tasks with a limited amount of delete information. This is done by introducing special fluents that explicitly represent conjunctions of fluents in the original planning task, rendering h+ the perfect heuristic h* in the limit. Previous work has introduced a method in which the growth of the task is potentially exponential in the number of conjunctions introduced. We formulate an alternative technique relying on conditional effects, limiting the growth of the task to be linear in this number. We show that this method still renders h+ the perfect heuristic h* in the limit. We propose techniques to find an informative set of conjunctions to be introduced in different settings, and analyze and extend existing methods for lower-bounding and upper-bounding h + in the presence of conditional effects. We evaluate the resulting heuristic functions empirically on a set of IPC benchmarks, and show that they are sometimes much more informative than standard delete-relaxation heuristics

A More General Theory of Diagnosis from First Principles

Model-based diagnosis has been an active research topic in different communities including artificial intelligence, formal methods, and control. This has led to a set of disparate approaches addressing different classes of systems and seeking different forms of diagnoses. In this paper, we resolve such disparities by generalising Reiter's theory to be agnostic to the types of systems and diagnoses considered. This more general theory of diagnosis from first principles defines the minimal diagnosis as the set of preferred diagnosis candidates in a search space of hypotheses. Computing the minimal diagnosis is achieved by exploring the space of diagnosis hypotheses, testing sets of hypotheses for consistency with the system's model and the observation, and generating conflicts that rule out successors and other portions of the search space. Under relatively mild assumptions, our algorithms correctly compute the set of preferred diagnosis candidates. The main difficulty here is that the search space is no longer a powerset as in Reiter's theory, and that, as consequence, many of the implicit properties (such as finiteness of the search space) no longer hold. The notion of conflict also needs to be generalised and we present such a more general notion. We present two implementations of these algorithms, using test solvers based on satisfiability and heuristic search, respectively, which we evaluate on instances from two real world discrete event problems. Despite the greater generality of our theory, these implementations surpass the special purpose algorithms designed for discrete event systems, and enable solving instances that were out of reach of existing diagnosis approaches

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

Incremental Lower Bounds for Additive Cost Planning Problems

We present a novel method for computing increasing lower bounds on the cost of solving planning problems, based on repeatedly solving and strengthening the delete relaxation of the problem. Strengthening is done by compiling select conjunctions into new atoms, similar to theP m ⋆ construction. Because it does not rely on search in the state space, this method does not suffer some of the weaknesses of admissible search algorithms and therefore is able to prove higher lower bounds for many problems that are too hard for optimal planners to solve, thus narrowing the gap between lower bound and cost of the best known plan, providing better assurances of plan quality

Conflict-driven learning in AI planning state-space search

Many combinatorial computation problems in computer science can be cast as a reachability problem in an implicitly described, potentially huge, graph: the state space. State-space search is a versatile and widespread method to solve such reachability problems, but it requires some form of guidance to prevent exploring that combinatorial space exhaustively. Conflict-driven learning is an indispensable search ingredient for solving constraint satisfaction problems (most prominently, Boolean satisfiability). It guides search towards solutions by identifying conflicts during the search, i.e., search branches not leading to any solution, learning from them knowledge to avoid similar conflicts in the remainder of the search. This thesis adapts the conflict-driven learning methodology to more general classes of reachability problems. Specifically, our work is placed in AI planning. We consider goal-reachability objectives in classical planning and in planning under uncertainty. The canonical form of "conflicts" in this context are dead-end states, i.e., states from which the desired goal property cannot be reached. We pioneer methods for learning sound and generalizable dead-end knowledge from conflicts encountered during forward state-space search. This embraces the following core contributions: When acting under uncertainty, the presence of dead-end states may make it impossible to satisfy the goal property with absolute certainty. The natural planning objective then is MaxProb, maximizing the probability of reaching the goal. However, algorithms for MaxProb probabilistic planning are severely underexplored. We close this gap by developing a large design space of probabilistic state-space search methods, contributing new search algorithms, admissible state-space reduction techniques, and goal-probability bounds suitable for heuristic state-space search. We systematically explore this design space through an extensive empirical evaluation. The key to our conflict-driven learning algorithm adaptation are unsolvability detectors, i.e., goal-reachability overapproximations. We design three complementary families of such unsolvability detectors, building upon known techniques: critical-path heuristics, linear-programming-based heuristics, and dead-end traps. We develop search methods to identify conflicts in deterministic and probabilistic state spaces, and we develop suitable refinement methods for the different unsolvability detectors so to recognize these states. Arranged in a depth-first search, our techniques approach the elegance of conflict-driven learning in constraint satisfaction, featuring the ability to learn to refute search subtrees, and intelligent backjumping to the root cause of a conflict. We provide a comprehensive experimental evaluation, demonstrating that the proposed techniques yield state-of-the-art performance for finding plans for solvable classical planning tasks, proving classical planning tasks unsolvable, and solving MaxProb in probabilistic planning, on benchmarks where dead-end states abound.Viele kombinatorisch komplexe Berechnungsprobleme in der Informatik lassen sich als Erreichbarkeitsprobleme in einem implizit dargestellten, potenziell riesigen, Graphen - dem Zustandsraum - verstehen. Die Zustandsraumsuche ist eine weit verbreitete Methode, um solche Erreichbarkeitsprobleme zu lösen. Die Effizienz dieser Methode hängt aber maßgeblich von der Verwendung strikter Suchkontrollmechanismen ab. Das konfliktgesteuerte Lernen ist eine essenzielle Suchkomponente für das Lösen von Constraint-Satisfaction-Problemen (wie dem Erfüllbarkeitsproblem der Aussagenlogik), welches von Konflikten, also Fehlern in der Suche, neue Kontrollregeln lernt, die ähnliche Konflikte zukünftig vermeiden. In dieser Arbeit erweitern wir die zugrundeliegende Methodik auf Zielerreichbarkeitsfragen, wie sie im klassischen und probabilistischen Planen, einem Teilbereich der Künstlichen Intelligenz, auftauchen. Die kanonische Form von „Konflikten“ in diesem Kontext sind sog. Sackgassen, Zustände, von denen aus die Zielbedingung nicht erreicht werden kann. Wir präsentieren Methoden, die es ermöglichen, während der Zustandsraumsuche von solchen Konflikten korrektes und verallgemeinerbares Wissen über Sackgassen zu erlernen. Unsere Arbeit umfasst folgende Beiträge: Wenn der Effekt des Handelns mit Unsicherheiten behaftet ist, dann kann die Existenz von Sackgassen dazu führen, dass die Zielbedingung nicht unter allen Umständen erfüllt werden kann. Die naheliegendste Planungsbedingung in diesem Fall ist MaxProb, das Maximieren der Wahrscheinlichkeit, dass die Zielbedingung erreicht wird. Planungsalgorithmen für MaxProb sind jedoch wenig erforscht. Um diese Lücke zu schließen, erstellen wir einen umfangreichen Bausatz für Suchmethoden in probabilistischen Zustandsräumen, und entwickeln dabei neue Suchalgorithmen, Zustandsraumreduktionsmethoden, und Abschätzungen der Zielerreichbarkeitswahrscheinlichkeit, wie sie für heuristische Suchalgorithmen gebraucht werden. Wir explorieren den resultierenden Gestaltungsraum systematisch in einer breit angelegten empirischen Studie. Die Grundlage unserer Adaption des konfliktgesteuerten Lernens bilden Unerreichbarkeitsdetektoren. Wir konzipieren drei Familien solcher Detektoren basierend auf bereits bekannten Techniken: Kritische-Pfad Heuristiken, Heuristiken basierend auf linearer Optimierung, und Sackgassen-Fallen. Wir entwickeln Suchmethoden, um Konflikte in deterministischen und probabilistischen Zustandsräumen zu erkennen, sowie Methoden, um die verschiedenen Unerreichbarkeitsdetektoren basierend auf den erkannten Konflikten zu verfeinern. Instanziiert als Tiefensuche weisen unsere Techniken ähnliche Eigenschaften auf wie das konfliktgesteuerte Lernen für Constraint-Satisfaction-Problemen. Wir evaluieren die entwickelten Methoden empirisch, und zeigen dabei, dass das konfliktgesteuerte Lernen unter gewissen Voraussetzungen zu signifikanten Suchreduktionen beim Finden von Plänen in lösbaren klassischen Planungsproblemen, Beweisen der Unlösbarkeit von klassischen Planungsproblemen, und Lösen von MaxProb im probabilistischen Planen, führen kann