An LP-Based Approach for Goal Recognition as Planning

Goal recognition aims to recognize the set of candidate goals that are compatible with the observed behavior of an agent. In this paper, we develop a method based on the operator-counting framework that efficiently computes solutions that satisfy the observations and uses the information generated to solve goal recognition tasks. Our method reasons explicitly about both partial and noisy observations: estimating uncertainty for the former, and satisfying observations given the unreliability of the sensor for the latter. We evaluate our approach empirically over a large data set, analyzing its components on how each can impact the quality of the solutions. In general, our approach is superior to previous methods in terms of agreement ratio, accuracy, and spread. Finally, our approach paves the way for new research on combinatorial optimization to solve goal recognition tasks.Comment: 8 pages, 4 tables, 3 figures. Published in AAAI 2021. Updated final authorship and tex

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

Cost Partitioning Heuristics for Stochastic Shortest Path Problems

In classical planning, cost partitioning is a powerful method which allows to combine multiple admissible heuristics while retaining an admissible bound. In this paper, we extend the theory of cost partitioning to probabilistic planning by generalizing from deterministic transition systems to stochastic shortest path problems (SSPs). We show that fundamental results related to cost partitioning still hold in our extended theory. We also investigate how to optimally partition costs for a large class of abstraction heuristics for SSPs. Lastly, we analyze occupation measure heuristics for SSPs as well as the theory of approximate linear programming for reward-oriented Markov decision processes. All of these fit our framework and can be seen as cost-partitioned heuristics

ADDMC: Weighted Model Counting with Algebraic Decision Diagrams

We present an algorithm to compute exact literal-weighted model counts of Boolean formulas in Conjunctive Normal Form. Our algorithm employs dynamic programming and uses Algebraic Decision Diagrams as the primary data structure. We implement this technique in ADDMC, a new model counter. We empirically evaluate various heuristics that can be used with ADDMC. We then compare ADDMC to state-of-the-art exact weighted model counters (Cachet, c2d, d4, and miniC2D) on 1914 standard model counting benchmarks and show that ADDMC significantly improves the virtual best solver.Comment: Presented at AAAI 202

PrIC3: Property Directed Reachability for MDPs

IC3 has been a leap forward in symbolic model checking. This paper proposes PrIC3 (pronounced pricy-three), a conservative extension of IC3 to symbolic model checking of MDPs. Our main focus is to develop the theory underlying PrIC3. Alongside, we present a first implementation of PrIC3 including the key ingredients from IC3 such as generalization, repushing, and propagation