Efficient Evaluation of Large Abstractions for Decoupled Search: Merge-and-Shrink and Symbolic Pattern Databases

Abstraction heuristics are a state-of-the-art technique to solve classical planning problems optimally. A common approach is to precompute many small abstractions and combine them admissibly using cost partitioning. Recent work has shown that this approach does not work out well when using such heuristics for decoupled state space search, where search nodes represent potentially large sets of states. This is due to the fact that admissibly combining the estimates of several heuristics without sacrificing accuracy is NP-hard for decoupled states. In this work we propose to use a single large abstraction instead. We focus on merge-and-shrink and symbolic pattern database heuristics, which are designed to produce such abstractions. For these heuristics, we prove that the evaluation of decoupled states is NP-hard in general, but we also identify conditions under which it is polynomial. We introduce algorithms for both the general and the polynomial case. Our experimental evaluation shows that single large abstraction heuristics lead to strong performance when the heuristic evaluation is polynomial

Narrowing the Gap Between Saturated and Optimal Cost Partitioning for Classical Planning

In classical planning, cost partitioning is a method for admissibly combining a set of heuristic estimators by distributing operator costs among the heuristics. An optimal cost partitioning is often prohibitively expensive to compute. Saturated cost partitioning is an alternative that is much faster to compute and has been shown to offer high-quality heuristic guidance on Cartesian abstractions. However, its greedy nature makes it highly susceptible to the order in which the heuristics are considered. We show that searching in the space of orders leads to significantly better heuristic estimates than with previously considered orders. Moreover, using multiple orders leads to a heuristic that is significantly better informed than any single-order heuristic. In experiments with Cartesian abstractions, the resulting heuristic approximates the optimal cost partitioning very closely

A Comparison of Cost Partitioning Algorithms for Optimal Classical Planning

Cost partitioning is a general and principled approach for constructing additive admissible heuristics for state-space search. Cost partitioning approaches for optimal classical planning include optimal cost partitioning, uniform cost partitioning, zero-one cost partitioning, saturated cost partitioning, post-hoc optimization and the canonical heuristic for pattern databases. We compare these algorithms theoretically, showing that saturated cost partitioning dominates greedy zero-one cost partitioning. As a side effect of our analysis, we obtain a new cost partitioning algorithm dominating uniform cost partitioning. We also evaluate these algorithms experimentally on pattern databases, Cartesian abstractions and landmark heuristics, showing that saturated cost partitioning is usually the method of choice on the IPC benchmark suite

Symbolic search and abstraction heuristics for cost-optimal planning in automated planning

Mención Internacional en el título de doctorLa Planificación Automática puede ser definida como el problema de encontrar una secuencia de acciones (un plan) para conseguir una meta, desde un punto inicial, asumiendo que las acciones tienen efectos deterministas. La Planificación Automática es independiente de dominio porque los planificadores toman como información inicial una descripción del problema y deben resolverlo sin ninguna información adicional. Esta tesis trata en particular de planificación automática ´optima, en la cual las acciones tienen un coste asociado. Los planificadores óptimos deben encontrar un plan y probar que no existe ningún otro plan de menor coste. La mayoría de los planificadores óptimos están basados en la búsqueda de estados explícita. Sin lugar a dudas, esta aproximación ha sido la dominante en planificación automática óptima durante los últimos años. No obstante, la búsqueda simbólica se presenta como una alternativa interesante. En esta tesis, proponemos dos mejoras ortogonales para la planificación basada en búsqueda simbólica. En primer lugar, estudiamos diferentes métodos para mejorar la computación de la “imagen”, operación que calcula el conjunto de estados sucesores a partir de un conjunto de estados. Posteriormente, analizamos cómo explotar las invariantes de estado para mejorar el rendimiento de la búsqueda simbólica. Estas propuestas suponen una mejora significativa en el desempeño de los algoritmos simbólicos en la mayoría de los dominios analizados. Hemos analizado dos tipos de heurísticas de abstracción con el objetivo de extrapolar las mejoras que se han realizado en la búsqueda explícita durante los últimos años a la búsqueda simbólica. Las heurísticas analizadas son: las bases de datos de patrones (pattern databases, PDBs) y una generalización de estas, mergeand-shrink (M&S). Mientras que las PDBs se han utilizado con anterioridad en búsqueda simbólica, hemos estudiado el uso de M&S, que es más general. En esta tesis se muestra que determinados tipos de heurísticas de M&S (aquellas que son generadas mediante una estrategia de “merge” lineal) pueden ser representadas como BDDs, con un coste computacional polinomial en el tamaño de la abstracción y la descripción del problema; y por lo tanto, pueden ser utilizadas de forma eficiente en la búsqueda simbólica. También proponemos una nueva heurística”symbolic perimeter merge-andshrink” (SPM&S) que combina la fuerza de la búsqueda hacia atrás simbólica con la flexibilidad de M&S. Los resultados experimentales muestran que SPM&S es capaz de superar, no solo las dos técnicas que combina, sino también otras heurísticas del estado del arte. Finalmente, hemos integrado las abstracciones simbólicas de perímetro, SPM&S, en la búsqueda simbólica bidireccional. En resumen, esta tesis estudia diferentes propuestas para planificación óptima basada en Búsqueda simbólica. Hemos implementado diferentes planificadores simbólicos basados en la Búsqueda bidireccional y las abstracciones de perímetro. Los resultados experimentales muestran cómo los planificadores presentados como resultado de este trabajo son altamente competitivos y frecuentemente superan al resto de planificadores del estado del arte.Domain-independent planning is the problem of finding a sequence of actions for achieving a goal from an initial state assuming that actions have deterministic effects. It is domain-independent because planners take as input the description of a problem and must solve it without any additional information. In this thesis, we deal with cost-optimal planning problems, in which actions have an associated cost and the planner must find a plan and prove that no other plan of lower cost exists. Most cost-optimal planners are based on explicit-state search. While this has undoubtedly been the dominant approach to cost-optimal planning in the last years, symbolic search is an interesting alternative. In symbolic search, sets of states are succinctly represented as binary decision diagrams, BDDs. The BDD representation does not only reduce the memory needed to store sets of states, but also allows the planner to efficiently manipulate sets of states reducing the search time. We propose two orthogonal enhancements for symbolic search planning. On the one hand, we study different methods for image computation, which usually is the bottleneck of symbolic search planners. On the other hand, we analyze how to exploit state invariants to prune symbolic search. Our techniques significantly improve the performance of symbolic search algorithms in most benchmark domains. Moreover, the enhanced version of symbolic bidirectional search is one of the strongest approaches to domain-independent planning even though it does not use any heuristic. Explicit-state search planners are commonly guided with admissible heuristics, which optimistically estimate the cost from any state to the goal. Heuristics are automatically derived from the problem description and can be classified into different families according to their underlying ideas. In order to bring the improvements on heuristics that have been made in explicit-state search to symbolic search, we analyze two types of abstraction heuristics: pattern databases (PDBs) and a generalization of them, merge-and-shrink (M&S). While PDBs had already been used in symbolic search, we analyze the use of the more general M&S heuristics. We show that certain types of M&S heuristics (those generated with a linear merging strategy) can be represented as BDDs with at most a polynomial overhead and, thus, efficiently used in symbolic search. We also propose a new heuristic, symbolic perimeter merge-and-shrink (SPM&S) that combines the strength of symbolic regression search with the flexibility of M&S heuristics. Our experiments show that SPM&S is able to beat, not only the two techniques it combines, but also other state-of-the-art heuristics. Finally, we integrate our symbolic perimeter abstraction heuristics in symbolic bidirectional search. The heuristic used by the bidirectional search is computed by means of another symbolic bidirectional search in an abstract state space. We show how, even though the combination of symbolic bidirectional search and abstraction heuristics has an overall performance similar to the simpler symbolic bidirectional blind search, it can sometimes solve more problems in particular domains. In summary, this thesis studies different enhancements on symbolic search. We implement different symbolic search planners based on bidirectional search and perimeter abstraction heuristics. Experimental results show that the resulting planners are highly competitive and often outperform other state-of-the-art planners.Programa Oficial de Doctorado en Ciencia y Tecnología InformáticaPresidente: José Manuel Molina López..- Vocal: Malte Helmert .- Secretario: Andrés Jonsso

Online Planner Selection with Graph Neural Networks and Adaptive Scheduling

Automated planning is one of the foundational areas of AI. Since no single planner can work well for all tasks and domains, portfolio-based techniques have become increasingly popular in recent years. In particular, deep learning emerges as a promising methodology for online planner selection. Owing to the recent development of structural graph representations of planning tasks, we propose a graph neural network (GNN) approach to selecting candidate planners. GNNs are advantageous over a straightforward alternative, the convolutional neural networks, in that they are invariant to node permutations and that they incorporate node labels for better inference. Additionally, for cost-optimal planning, we propose a two-stage adaptive scheduling method to further improve the likelihood that a given task is solved in time. The scheduler may switch at halftime to a different planner, conditioned on the observed performance of the first one. Experimental results validate the effectiveness of the proposed method against strong baselines, both deep learning and non-deep learning based. The code is available at \url{https://github.com/matenure/GNN_planner}.Comment: AAAI 2020. Code is released at https://github.com/matenure/GNN_planner. Data set is released at https://github.com/IBM/IPC-graph-dat

On Solving the Rubik's Cube with Domain-Independent Planners Using Standard Representations

Rubik's Cube (RC) is a well-known and computationally challenging puzzle that has motivated AI researchers to explore efficient alternative representations and problem-solving methods. The ideal situation for planning here is that a problem be solved optimally and efficiently represented in a standard notation using a general-purpose solver and heuristics. The fastest solver today for RC is DeepCubeA with a custom representation, and another approach is with Scorpion planner with State-Action-Space+ (SAS+) representation. In this paper, we present the first RC representation in the popular PDDL language so that the domain becomes more accessible to PDDL planners, competitions, and knowledge engineering tools, and is more human-readable. We then bridge across existing approaches and compare performance. We find that in one comparable experiment, DeepCubeA (trained with 12 RC actions) solves all problems with varying complexities, albeit only 78.5% are optimal plans. For the same problem set, Scorpion with SAS+ representation and pattern database heuristics solves 61.50% problems optimally, while FastDownward with PDDL representation and FF heuristic solves 56.50% problems, out of which 79.64% of the plans generated were optimal. Our study provides valuable insights into the trade-offs between representational choice and plan optimality that can help researchers design future strategies for challenging domains combining general-purpose solving methods (planning, reinforcement learning), heuristics, and representations (standard or custom)

Unsolvability Certificates for Classical Planning

The plans that planning systems generate for solvable planning tasks are routinely verified by independent validation tools. For unsolvable planning tasks, no such validation capabilities currently exist. We describe a family of certificates of unsolvability for classical planning tasks that can be efficiently verified and are sufficiently general for a wide range of planning approaches including heuristic search with delete relaxation, critical-path, pattern database and linear merge-and-shrink heuristics, symbolic search with binary decision diagrams, and the Trapper algorithm for detecting dead ends. We also augmented a classical planning system with the ability to emit certificates of unsolvability and implemented a planner-independent certificate validation tool. Experiments show that the overhead for producing such certificates is tolerable and that their validation is practically feasible

Simplified Planner Selection

There exists no planning algorithm that outperforms all oth- ers. Therefore, it is important to know which algorithm works well on a task. A recently published approach uses either im- age or graph convolutional neural networks to solve this prob- lem and achieves top performance. Especially the transforma- tion from the task to an image ignores a lot of information. Thus, we would like to know what the network is learning and if this is reasonable. As this is currently not possible, we take one step back. We identify a small set of simple graph features and show that elementary and interpretable machine learning techniques can use those features to outperform the neural network based approach. Furthermore, we evaluate the importance of those features and verify that the performance of our approach is robust to changes in the training and test data

Explainable Planner Selection

Since no classical planner consistently outperforms all oth ers, it is important to select a planner that works well for a given classical planning task. The two strongest approaches for planner selection use image and graph convolutional neu ral networks. They have the drawback that the learned mod els are not interpretable. To obtain explainable models, we identify a small set of simple task features and show that el ementary and interpretable machine learning techniques can use these features to solve as many tasks as the approaches based on neural networks