Focusing on What Really Matters: Irrelevance Pruning in M&S ´ Alvaro Torralba, Peter Kissmann Saarland University, Germany SoCS 2015, June 11 Session with ICAPS 2015 Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 1 / 16
Motivation: Irrelevance Pruning Last Tuesday: h 2 -based preprocessor Simplify the task in a preprocessing step Remove operators that cannot possibly belong to any plan Very useful!!!! Today: Can we simplify the tasks even further? Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 2 / 16
Motivation: Irrelevance Pruning Last Tuesday: h 2 -based preprocessor Simplify the task in a preprocessing step Remove operators that cannot possibly belong to any plan Very useful!!!! Today: Can we simplify the tasks even further? B C T A D I G G I E A B C D E (Truck) (Package) Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 2 / 16
Motivation: Irrelevance Pruning Last Tuesday: h 2 -based preprocessor Simplify the task in a preprocessing step Remove operators that cannot possibly belong to any plan Very useful!!!! Today: Can we simplify the tasks even further? B C T A D I G G I E A B C D E (Truck) (Package) Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 2 / 16
Merge-and-Shrink Heuristic An admissible abstraction heuristic for cost-optimal planning Start with the projection over variables: v 1 , v 2 , v 3 , v 4 1 Merge: replace Θ i and Θ j by their product 2 Shrink: replace Θ i by its abstraction α (Θ i ) 3 L Θ 1 Θ 2 Θ 3 Θ 4 Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 3 / 16
Merge-and-Shrink Heuristic An admissible abstraction heuristic for cost-optimal planning Start with the projection over variables: v 1 , v 2 , v 3 , v 4 1 Merge: replace Θ i and Θ j by their product 2 Shrink: replace Θ i by its abstraction α (Θ i ) 3 L Θ 1 ⊗ Θ 2 Θ 3 Θ 4 Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 3 / 16
Merge-and-Shrink Heuristic An admissible abstraction heuristic for cost-optimal planning Start with the projection over variables: v 1 , v 2 , v 3 , v 4 1 Merge: replace Θ i and Θ j by their product 2 Shrink: replace Θ i by its abstraction α (Θ i ) 3 L Θ 1 ⊗ Θ 2 Θ 3 ⊗ Θ 4 Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 3 / 16
Merge-and-Shrink Heuristic An admissible abstraction heuristic for cost-optimal planning Start with the projection over variables: v 1 , v 2 , v 3 , v 4 1 Merge: replace Θ i and Θ j by their product 2 Shrink: replace Θ i by its abstraction α (Θ i ) 3 L α 1 , 2 α 3 , 4 Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 3 / 16
Merge-and-Shrink Heuristic An admissible abstraction heuristic for cost-optimal planning Start with the projection over variables: v 1 , v 2 , v 3 , v 4 1 Merge: replace Θ i and Θ j by their product 2 Shrink: replace Θ i by its abstraction α (Θ i ) 3 L α 1 , 2 ⊗ α 3 , 4 Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 3 / 16
Simulation-Based Dominance Pruning Label-dominance simulation (Torralba and Hoffmann, IJCAI 2015): Use M&S to compute a partition of the problem: { Θ 1 , . . . , Θ k } 1 Compute label-dominance simulation relation: {� 1 , . . . , � k } 2 Label dominance: l dominates l ′ in Θ i if for any s l l ′ − → t exists s − → t ′ s.t. t � t ′ l ′ l → t ′ s.t.: State dominance s � t : For any s − → s ′ , exists t − t � t ′ c ( l ′ ) ≤ c ( l ) l ′ dominates l in the rest of the problem In A ∗ , prune any s s.t. s � t , g ( s ) ≥ g ( t ) for some t 3 Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 4 / 16
Merge-and-Shrink Framework (Sievers et al. 2014) Θ 1 Θ 2 Θ 3 Θ 4 Global Θ Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 5 / 16
Merge-and-Shrink Framework (Sievers et al. 2014) FDR task: �V , O , I , G� v 1 v 2 v 3 v 4 State space Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 5 / 16
Merge-and-Shrink Framework (Sievers et al. 2014) Θ 1 Θ 2 Θ 3 Θ 4 Global Θ M&S: Framework for transformation of planning tasks Operation Merge Shrink Exact Label Reduction Bisimulation shrinking Reachability pruning Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 5 / 16
Merge-and-Shrink Framework (Sievers et al. 2014) Θ 1 Θ 2 Θ 3 Θ 4 Global Θ M&S: Framework for transformation of planning tasks Operation Transformation to global LTS Merge None Shrink Abstraction Exact Label Reduction Change labels Preserves h ∗ Bisimulation shrinking Reachability pruning Keeps reachable/solvable part Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 5 / 16
Merge-and-Shrink Framework (Sievers et al. 2014) Θ 1 Θ 2 Θ 3 Θ 4 Global Θ M&S: Framework for transformation of planning tasks Operation Transformation to global LTS Merge None Shrink Abstraction Exact Label Reduction Change labels Preserves h ∗ Bisimulation shrinking Reachability pruning Keeps reachable/solvable part Subsumed transition pruning Preserves h ∗ Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 5 / 16
Plan Preserving Transformations of Planning Tasks Plan preserving Π ′ Π Plan preserving: Does not add any new optimal plan to the task 1 At least one optimal plan for the original task is preserved ( h ∗ ( I ) ) 2 Unreachable/dead-end pruning is plan preserving In this paper: subsumed transition pruning → remove transitions from M&S transition systems → globally h -preserving ( h ∗ ( s ) for every s ) Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 6 / 16
Subsumed Transition Pruning Definition (Subsumed transition) l ′ l → t ′ s i − → t i is subsumed by s i − i if: t i � t ′ i and 1 c ( l ′ ) ≤ c ( l ) and 2 l ′ dominates l in all Θ j for j � = i . 3 Thm: Remove subsumed transitions is globally h -preserving Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 7 / 16
Subsumed Transition Pruning Definition (Subsumed transition) l ′ l → t ′ s i − → t i is subsumed by s i − i if: t i � t ′ i and 1 c ( l ′ ) ≤ c ( l ) and 2 l ′ dominates l in all Θ j for j � = i . 3 Thm: Remove subsumed transitions is globally h -preserving B C A D I E G Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 7 / 16
Subsumed Transition Pruning Definition (Subsumed transition) l ′ l → t ′ s i − → t i is subsumed by s i − i if: t i � t ′ i and 1 c ( l ′ ) ≤ c ( l ) and 2 l ′ dominates l in all Θ j for j � = i . 3 Thm: Remove subsumed transitions is globally h -preserving B C I → A is subsumed by I → E A D G → D is subsumed by G → E I E G Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 7 / 16
Subsumed Transition Pruning Definition (Subsumed transition) l ′ l → t ′ s i − → t i is subsumed by s i − i if: t i � t ′ i and 1 c ( l ′ ) ≤ c ( l ) and 2 l ′ dominates l in all Θ j for j � = i . 3 Thm: Remove subsumed transitions is globally h -preserving B C I → A is subsumed by I → E A D G → D is subsumed by G → E I E G A, B, C, D become unreachable Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 7 / 16
Example: Subsumed Transition Pruning Θ 1 ⊗ Θ 2 : Θ 1 : l l s 1 t 1 ( s 1 , s 2 ) ( s 1 , t 2 ) l l ′ l l ′ Θ 2 : l l ′ s 2 t 2 l ′ ( t 1 , s 2 ) ( t 1 , t 2 ) l ′ Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 8 / 16
Example: Subsumed Transition Pruning Θ 1 ⊗ Θ 2 : Θ 1 : l l s 1 t 1 ( s 1 , s 2 ) ( s 1 , t 2 ) l l ′ l l ′ Θ 2 : l l ′ s 2 t 2 l ′ ( t 1 , s 2 ) ( t 1 , t 2 ) l ′ l l ′ s 1 − → t 1 is subsumed by s 1 − → t 1 Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 8 / 16
Example: Subsumed Transition Pruning Θ 1 ⊗ Θ 2 : Θ 1 : l l s 1 t 1 ( s 1 , s 2 ) ( s 1 , t 2 ) l l ′ l l ′ Θ 2 : l l ′ s 2 t 2 l ′ ( t 1 , s 2 ) ( t 1 , t 2 ) l ′ l l ′ s 1 − → t 1 is subsumed by s 1 → t 1 − l ′ l − → t 2 is subsumed by s 2 − → t 2 s 2 Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 8 / 16
Example: Subsumed Transition Pruning Θ 1 ⊗ Θ 2 : Θ 1 : l l s 1 t 1 ( s 1 , s 2 ) ( s 1 , t 2 ) l l ′ l l ′ Θ 2 : l l ′ s 2 t 2 l ′ ( t 1 , s 2 ) ( t 1 , t 2 ) l ′ l l ′ s 1 − → t 1 is subsumed by s 1 → t 1 − l ′ l − → t 2 is subsumed by s 2 − → t 2 s 2 Don’t remove a transition if the label dominance changes! Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 8 / 16
Taking Advantage of Plan-Preserving Transformations Search task Π ′ instead of Π 1 implementation overhead (future work) Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 9 / 16
Taking Advantage of Plan-Preserving Transformations Search task Π ′ instead of Π 1 implementation overhead (future work) Remove dead operators: 2 after subsumed transition and unreachability pruning Torralba, Kissmann From Dominance to Irrelevance Pruning SoCS 2015 9 / 16
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