Counterexample-Guided Cartesian Abstraction Refinement for Classical Planning

Seipp, Jendrik; Helmert, Malte

doi:10.1613/jair.1.11217

Cited by 52 publications

(91 citation statements)

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“…Variable projection is a fairly coarse abstraction method, and another method which allows for a more fine grained control is cartesian abstraction [SH13], and variable projection is a special case of it. Seipp and Helmert [SH13] use cartesian abstraction in roughly the following way: (1) find a solution for the abstract instance, if there is none then the original instance is unsolvable; (2) find a flaw in the solution by applying it on the original instance, if there is none then we have found a solution for the original instance; (3) adjust the abstraction to resolve the flaw; (4) if we are not satisfied with the current abstraction then go to (1), otherwise we are done.…”

Section: Cegarmentioning

confidence: 99%

“…Seipp and Helmert [SH13] use cartesian abstraction in roughly the following way: (1) find a solution for the abstract instance, if there is none then the original instance is unsolvable; (2) find a flaw in the solution by applying it on the original instance, if there is none then we have found a solution for the original instance; (3) adjust the abstraction to resolve the flaw; (4) if we are not satisfied with the current abstraction then go to (1), otherwise we are done. In other words, this algorithm, also known as counterexample-guided cartesian abstraction refinement (CEGAR), disproves abstract solutions.…”

Section: Cegarmentioning

confidence: 99%

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Methods for Detecting Unsolvable Planning Instances using Variable Projection

Ståhlberg¹

2017

Linköping Studies in Science and Technology. Dissertations

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In this thesis we study automated planning, a branch of artificial intelligence, which deals with the construction of plans. A plan is typically an action sequence that achieves some specific goal. In particular, we study unsolvable planning instances, i.e. when there is no plan. Historically, this topic has been neglected by the planning community, and up to recently the International Planning Competition only evaluated planners on solvable planning instances. For many applications we can know, for instance by design, that there is a solution, but this cannot be a general assumption. One example is penetration testing in computer security, where a system is considered safe if there is no plan for intrusion. Other examples are resource bounded planning instances that have insufficient resources to achieve the goal.The main theme of this thesis is to use variable projection to prove unsolvability of planning instances. We implement and evaluate two planners: the first checks variable projections with the goal of finding an unsolvable projection, and the second builds a pattern collection to provide dead-end detection. In addition to comparing these planners to existing planners, we also utilise a large computer cluster to statistically assess whether they can be optimised further. On the benchmarks of planning instances that we used, it turns out that further improvement is likely to come from supplementary techniques rather than further optimisation. We pursue this and enhanced variable projections with mutexes, which yields a very competitive planner. We also inspect whether unsolvable variable projections tend to be composed of variables that play different roles, i.e. they are not 'similar'. We devise a variable similarity measure to rate how similar two variables are, and statistically analyse this. The measure can differentiate between unsolvable and solvable planning instances quite well, and is integrated into our planners. We also define a binary version of the measure, namely, that two variables are isomorphic if they behave in exactly the same way in some optimal solution (extremely similar). With the help of isomorphic variables we identify a computationally tractable class of planning instances that meet certain restrictions. There are several special cases of this class that are of practical interest, and this result encompass them. This work has been supported by the Theoretical Computer Science Laboratory, Department of Computer and Information Science, Linköping University, and in part by CUGS (the National Graduate School in Computer Science, Sweden).i Populärvetenskaplig sammanfattningI den här avhandlingen studerar vi automatisk planering, vilket är ett nyckelområde inom artificiell intelligens. Planering är att tänka innan man handlar för att uppnå ett specificerat mål. Motsatsen till detta är att enbart handla reaktivt på vad som sker ögonblickligen. Planering använder sig av kunskap om världen för att konstruera en plan för vad som behöver göras, och i vilken ordning. Normalt tar vi...

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Section: Cegarmentioning

confidence: 99%

Section: Cegarmentioning

confidence: 99%

Methods for Detecting Unsolvable Planning Instances using Variable Projection

Ståhlberg¹

2017

Linköping Studies in Science and Technology. Dissertations

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“…Given that the number of states in a planning task is exponential in its size, the question arises how an abstraction -a partition of the state space -should be represented. Available answers are pattern databases (Culberson and Schaeffer 1998;Edelkamp 2001;, where an abstraction is defined in terms of a state-variable subset projected onto; merge-and-shrink abstraction (Dräger, Finkbeiner, and Podelski 2006;Helmert, Haslum, and Hoffmann 2007;Helmert et al 2014), which computes arbitrary abstractions by iteratively merging state variables and abstracting (shrinking) the product; and Cartesian abstraction (Ball, Podelski, and Rajamani 2001;Seipp and Helmert 2013), where abstract states are restricted to be cross-products of state-variable domain subsets.…”

Section: Cartesian Abstraction Heuristicsmentioning

confidence: 99%

“…cluding the approximation of goal distance (e.g. Edelkamp 2001;Haslum et al 2007;Seipp and Helmert 2013;Helmert et al 2014). In this paper, we explore abstract state spaces that are quotient graphs of the state space, where abstract states are blocks in a state partition, and the goal distance estimate for any state is the distance of its block to the nearest goal block.…”

Section: Introductionmentioning

confidence: 99%

“…These strategies are, per se, agnostic of how the abstraction is represented and how refinement operations are realized. Where relevant, we discuss these questions for Cartesian abstraction, which assumes a representation of the state space in terms of state variables, and restricts blocks to be cross-products of statevariable domain subsets (Ball, Podelski, and Rajamani 2001;Seipp and Helmert 2013). Cartesian abstraction allows finegrained state partitions yet supports effective refinement operations, and it underlies the current state of the art in using abstractions to design heuristic functions in planning (Seipp and Helmert 2014;Seipp 2017;Seipp and Helmert 2018).…”

Section: Introductionmentioning

confidence: 99%

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Refining Abstraction Heuristics during Real-Time Planning

Eifler

Fickert

Hoffmann

et al. 2019

AAAI

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In real-time planning, the planner must select the next action within a fixed time bound. Because a complete plan may not have been found, the selected action might not lead to a goal and the agent may need to return to its current state. To preserve completeness, real-time search methods incorporate learning, in which heuristic values are updated. Previous work in real-time search has used table-based heuristics, in which the values of states are updated individually. In this paper, we explore the use of abstraction-based heuristics. By refining the abstraction on-line, we can update the values of multiple states, including ones the agent has not yet generated. We test this idea empirically using Cartesian abstractions in the Fast Downward planner. Results on various benchmarks, including the sliding tile puzzle and several IPC domains, indicate that the approach can improve performance compared to traditional heuristic updating. This work brings abstraction refinement, a powerful technique from offline planning, into the real-time setting.

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Abstraction for Non-ground Answer Set Programs

Saribatur

Schüller

Eiter

2019

Logics in Artificial Intelligence

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ion is an important technique utilized by humans in model building and problem solving, in order to figure out key elements and relevant details of a world of interest. This naturally has led to investigations of using abstraction in AI and Computer Science to simplify problems, especially in the design of intelligent agents and automated problem solving. By omitting details, scenarios are reduced to ones that are easier to deal with and to understand, where further details are added back only when they matter. Despite the fact that abstraction is a powerful technique, it has not been considered much in the context of nonmonotonic knowledge representation and reasoning, and specifically not in Answer Set Programming (ASP), apart from some related simplification methods. In this work, we introduce a notion for abstracting from the domain of an ASP program such that the domain size shrinks while the set of answer sets (i.e., models) of the program is over-approximated. To achieve the latter, the program is transformed into an abstract program over the abstract domain while preserving the structure of the rules. We show in elaboration how this can be also achieved for single or multiple sub-domains (sorts) of a domain, and in case of structured domains like grid environments in which structure should be preserved. Furthermore, we introduce an abstraction-&-refinement methodology that makes it possible to start with an initial abstraction and to achieve automatically an abstraction with an associated abstract answer set that matches an answer set of the original program, provided that the program is satisfiable. Experiments based on prototypical implementations reveal the potential of the approach for problem analysis, by its ability to focus on the parts of the program that cause unsatisfiability and by achieving concrete abstract answer sets that merely reflect relevant details. This makes domain abstraction an interesting topic of research whose further use in important areas like Explainable AI remains to be explored.

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Counterexample-Guided Cartesian Abstraction Refinement for Classical Planning

Cited by 52 publications

References 0 publications

Methods for Detecting Unsolvable Planning Instances using Variable Projection

Methods for Detecting Unsolvable Planning Instances using Variable Projection

Refining Abstraction Heuristics during Real-Time Planning

Abstraction for Non-ground Answer Set Programs

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