How to Relax a Bisimulation?
Identifieur interne : 001949 ( Hal/Checkpoint ); précédent : 001948; suivant : 001950How to Relax a Bisimulation?
Auteurs : Michael Katz [France] ; Joerg Hoffmann [France] ; Malte Helmert [Suisse]Source :
Abstract
Merge-and-shrink abstraction (M&S) is an approach for constructing admissible heuristic functions for cost-optimal planning. It enables the targeted design of abstractions, by allowing to choose individual pairs of (abstract) states to aggregate into one. A key question is how to actually make these choices, so as to obtain an informed heuristic at reasonable computational cost. Recent work has addressed this via the well-known notion of bisimulation. When aggregating only bisimilar states -- essentially, states whose behavior is identical under every planning operator -- M&S yields a perfect heuristic. However, bisimulations are typically exponentially large. Thus we must relax the bisimulation criterion, so that it applies to more state pairs, and yields smaller abstractions. We herein devise a fine-grained method for doing so. We restrict the bisimulation criterion to consider only a subset K of the planning operators. We show that, if K is chosen appropriately, then M&S still yields a perfect heuristic, while abstraction size may decrease exponentially. Designing practical approximations for K, we obtain M&S heuristics that are competitive with the state of the art.
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<front><div type="abstract" xml:lang="en">Merge-and-shrink abstraction (M&S) is an approach for constructing admissible heuristic functions for cost-optimal planning. It enables the targeted design of abstractions, by allowing to choose individual pairs of (abstract) states to aggregate into one. A key question is how to actually make these choices, so as to obtain an informed heuristic at reasonable computational cost. Recent work has addressed this via the well-known notion of bisimulation. When aggregating only bisimilar states -- essentially, states whose behavior is identical under every planning operator -- M&S yields a perfect heuristic. However, bisimulations are typically exponentially large. Thus we must relax the bisimulation criterion, so that it applies to more state pairs, and yields smaller abstractions. We herein devise a fine-grained method for doing so. We restrict the bisimulation criterion to consider only a subset K of the planning operators. We show that, if K is chosen appropriately, then M&S still yields a perfect heuristic, while abstraction size may decrease exponentially. Designing practical approximations for K, we obtain M&S heuristics that are competitive with the state of the art.</div>
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<hal api="V3"><titleStmt><title xml:lang="en">How to Relax a Bisimulation?</title>
<author role="aut"><persName><forename type="first">Michael</forename>
<surname>Katz</surname>
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<author role="aut"><persName><forename type="first">Joerg</forename>
<surname>Hoffmann</surname>
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<email>joerg.hoffmann@loria.fr</email>
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<surname>Helmert</surname>
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<email>joerg.hoffmann@loria.fr</email>
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<editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2012-03-09 15:07:03</date>
<date type="whenModified">2015-09-22 01:12:56</date>
<date type="whenReleased">2012-03-09 15:07:42</date>
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<idno type="stamp" n="LORIA">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno>
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<sourceDesc><biblStruct><analytic><title xml:lang="en">How to Relax a Bisimulation?</title>
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<abstract xml:lang="en">Merge-and-shrink abstraction (M&S) is an approach for constructing admissible heuristic functions for cost-optimal planning. It enables the targeted design of abstractions, by allowing to choose individual pairs of (abstract) states to aggregate into one. A key question is how to actually make these choices, so as to obtain an informed heuristic at reasonable computational cost. Recent work has addressed this via the well-known notion of bisimulation. When aggregating only bisimilar states -- essentially, states whose behavior is identical under every planning operator -- M&S yields a perfect heuristic. However, bisimulations are typically exponentially large. Thus we must relax the bisimulation criterion, so that it applies to more state pairs, and yields smaller abstractions. We herein devise a fine-grained method for doing so. We restrict the bisimulation criterion to consider only a subset K of the planning operators. We show that, if K is chosen appropriately, then M&S still yields a perfect heuristic, while abstraction size may decrease exponentially. Designing practical approximations for K, we obtain M&S heuristics that are competitive with the state of the art.</abstract>
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