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State Agnostic Planning Graphs

State Agnostic Planning Graphs. William Cushing Daniel Bryce Arizona State University {william.cushing, dan.bryce}@asu.edu. Special thanks to: Subbarao Kambhampati, David E. Smith, Menkes van den Briel, Romeo Sanchez, J. Benton. p q r 6 7. q t r 5 6. p q r 5 6. r q p 5

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State Agnostic Planning Graphs

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  1. State Agnostic Planning Graphs William Cushing Daniel Bryce Arizona State University {william.cushing, dan.bryce}@asu.edu Special thanks to: Subbarao Kambhampati, David E. Smith, Menkes van den Briel, Romeo Sanchez, J. Benton

  2. p q r 6 7 q t r 5 6 p q r 5 6 r q p 5 6 p q r s t 5 6 7 p q r s t 6 7 8 q t r s p 5 6 7 r q p s t 5 6 7 Introduction ors ops ops oqs oqt opq opq orq opr opr oqr orp otp oqt oqt oqt o67 o67 o67 o78 o56 o67 o56 o56 1 3 3 5 )=5 h( 1 5 Motivation • Reachability analysis (via Planning Graphs) • Sets of planning graphs are useful • Progression search • Belief-space planning • Replanning • Robustification • Local search • … • …but highly redundant • PGs overlap (duplicate information) • PGs are inflexible (fixed source) • Generalize PG to multiple sources 1 1 1 o12 o12 q 5 2 2 G oG o23 3 3 3 o34 o34 4 4 o45 r 5 5 q5 p 5 G G G oG oG oG opq 3 3 3 o34 o34 opr 4 4 p5 r5 o45 p 6 5 5 5 o56 o56 o56 6 6 o67 7 p6 1 1 1 o12 o12 2 2 G oG o23 3 5 5 5 o56 o56 6 6 o67 7

  3. Introduction Overview State Agnostic Graph BuildSAG() ExtractH(A,B) ExtractH(A,B) Reachability Queries Planning Graphs BuildPG(A) Technique: Transform BuildPG(A) into BuildSAG() Labeled Uncertainty Graph [LUG] (Belief) State Agnostic LUG [SALUG] Optimized (Belief) State Agnostic LUG [SLUG] Scratch

  4. Heuristics for belief-space G  1 )=5 h( 3 3 5 1 5 Multiple Graphs 1 1 1 o12 o12 2 2 G oG o23 3 3 3 o34 o34 4 4 o45 5 G G G oG oG oG 3 3 3 o34 o34 4 4 o45 5 5 5 o56 o56 6 6 o67 7 1 1 1 o12 o12 2 2 G oG o23 3 5 5 5 o56 o56 6 6 o67 7 D. Bryce and S. Kambhampati, “Heuristic Guidance Measures for Conformant Planning”, In ICAPS’04, 2004.

  5. Heuristics for belief-space G  1 1 1 o12 o12 1 2 2 G G o23 oG oG 3 3 3 3 o34 o34 4 4 o45 1 1 1 5 o12 o12 G G G 2 2 oG oG o23 oG 3 5 1 1 1 1 o12 o12 2 2 G oG o23 5 3 5 5 5 o56 o56 6 6 o67 7 Unioned Graphs G oG 3 3 3 o34 o34 4 4 o45 5 5 5 o56 o56 6 6 o67 7

  6. Heuristics for belief-space G  1 )=1 h( 3 3 5 1 5 Unioned Graphs G G G oG oG oG 1 1 1 o12 o12 2 2 o23 3 3 3 3 o34 o34 4 4 o45 5 5 5 5 o56 o56 6 6 o67 7

  7. Heuristics for belief-space G  1 )=5 h( 3 3 5 1 5 Labeled Graph [LUG] G G G oG oG oG 1 1 1 o12 o12 2 2 o23 3 3 3 o34 o34 4 4 o45 5 5 5 o56 o56 6 6 o67 7 D. Bryce, S. Kambhampati, and D. Smith, “Planning in Belief Space with a Labelled Uncertainty Graph”, In AAAI Workshop on Markov Processes, 2004.

  8. Heuristics for belief-space G  1 G G G oG oG oG 3 1 1 1 o12 o12 2 2 o23 3 3 3 o34 o34 3 4 4 o45 5 5 5 5 o56 o56 6 6 o67 1 ^ 3 ^ -5 ^ γ 7 3 ^ 5 ^ -1 ^ γ 1 1 ^ 5 ^ -3 ^ γ 1 ^ 3v5 ^ -3v-5 ^ γ 5 3 ^ 1v5 ^ -1v-5 ^ γ 5 ^ 1v3 ^ -1v-3 ^ γ 1v3 ^ 3v5 ^ 1v5 ^ -1v-3v-5 ^ γ Labeled Graph [LUG] Binary Decision Diagrams Initialize: and/projection Operator: and/preconditions Literal: or/supporters D. Bryce, S. Kambhampati, and D. Smith, “Planning in Belief Space with a Labelled Uncertainty Graph”, In AAAI Workshop on Markov Processes, 2004. γ = “everything else false”

  9. Single graph for progression G G 1 1 1 G G G G oG oG oG oG oG oG 3 3 3 1 1 1 1 1 1 o12 o12 o12 o12 2 2 2 2 o23 o23 3 3 3 3 3 3 o34 o34 o34 o34 4 4 4 4 o45 o45 5 5 5 5 5 5 o56 o56 o56 o56 6 6 6 6 o67 o67 3 3 3 7 7 5 5 5 G G G G oG oG oG oG 1 1 1 1 1 1 1 1 1 o12 o12 o12 o12 2 2 2 2 o23 5 5 5 o23 3 3 3 3 3 3 o34 o34 o34 o34 4 4 4 4 o45 o45 5 5 5 5 5 5 o56 o56 o56 o56 6 6 6 6 o67 o67 7 7 Multiple (Labeled) Graphs D. Bryce, S. Kambhampati, and D. Smith, “Planning Graph Heuristics for Belief Space Search”, ASU CSE TR, 2005.

  10. Single graph for progression G G 1 1 1 1 G G G G oG oG oG oG oG oG 3 3 3 3 1 1 1 1 1 1 o12 o12 o12 o12 2 2 2 2 G G o23 o23 G 3 3 3 3 3 3 o34 o34 o34 o34 4 4 oG oG oG 4 4 o45 o45 5 5 5 5 5 5 o56 o56 o56 o56 6 6 6 6 o67 o67 3 3 3 3 7 7 1 1 1 o12 o12 2 2 5 5 5 5 o23 3 3 3 o34 o34 4 4 o45 G G 5 5 5 G G o56 o56 oG oG oG oG 6 6 1 1 1 1 o67 1 1 1 1 1 1 o12 o12 o12 o12 7 2 2 2 2 o23 5 5 5 5 o23 3 3 3 3 3 3 o34 o34 o34 o34 4 4 4 4 o45 o45 5 5 5 5 5 5 o56 o56 o56 o56 6 6 6 6 o67 o67 7 7 Unioned (Labeled) Graph

  11. Single graph for progression 3 1 1 5 5 3 Sr v Sb Sb v Sg Sr v Sg Sr^Sb^Sg => 1v3 ^ 3v5 ^ 1v5 ^ -1v-3v-5 ^ γ -Sr => 5 ^ 1v3 ^ -1v-3 ^ γ -Sb => 1 ^ 3v5 ^ -3v-5 ^ γ -Sg => 3 ^ 1v5 ^ -1v-5 ^ γ Labeled (Labeled) Graph [SALUG] Introduce labels for beliefs over labels for states G G G oG oG oG 1 1 1 o12 o12 2 2 o23 3 3 3 o34 o34 4 4 o45 5 5 5 o56 o56 6 6 o67 7 W. Cushing and D. Bryce, “State Agnostic Planning Graphs”, In AAAI, 2005.

  12. Single graph for progression Labeled (Labeled) Graph [SALUG] G G G oG oG oG 1 1 1 1 3 o12 o12 2 2 3 o23 3 3 3 5 o34 o34 4 4 o45 1 5 5 5 5 o56 o56 6 6 o67 7 W. Cushing and D. Bryce, “State Agnostic Planning Graphs”, In AAAI, 2005.

  13. Optimized single graph 1 3 3 5 1 5 Filtered Unioned (Labeled) Graph [SLUG] Don’t let the name fool you! G G G oG oG oG 1 1 1 o12 o12 2 2 o23 3 3 3 o34 o34 4 4 o45 5 5 5 o56 o56 6 6 o67 7 • Ignore irrelevant labels • Largest LUG == all LUGs W. Cushing and D. Bryce, “State Agnostic Planning Graphs”, In AAAI, 2005.

  14. Empirical Results Belief Space Problems ClassicalProblems Contingent Conformant

  15. Conclusion • Developed general agnosticism (SAG) • Removed dependence on world state (PG  LUG) • Removed dependence on belief state (LUG  SALUG) • Dramatically improved performance ({LUG,SALUG} ~> SLUG) • Empirically demonstrated • Internal performance boost • Favorable external comparison • SAG has rich connections to: • Constraint propagation (vs. branching) • Lazy evaluation • Memoization

  16. Further Details • Heuristics for belief space in the CAltAlt planner • D. Bryce and S. Kambhampati, “Heuristic Guidance Measures for Conformant Planning”, In ICAPS’04, 2004. • Labeled Uncertainty Graph in the CAltAlt planner • D. Bryce, S. Kambhampati, and D. Smith, “Planning in Belief Space with a Labelled Uncertainty Graph”, In AAAI Workshop on Markov Processes, 2004. • Heuristics and LUG in the POND and CAltAlt planners • D. Bryce, S. Kambhampati, and D. Smith, “Planning Graph Heuristics for Belief Space Search”, ASU CSE TR, 2005. • SLUG: Improvement to LUG for POND • W. Cushing and D. Bryce, “State Agnostic Planning Graphs”, In AAAI, 2005. • CLUG: propagating numeric information • D. Bryce and S. Kambhampati, “Cost Sensitive Reachability Heuristics for Handling State Uncertainty”, In UAI’05, 2005. http://rakaposhi.eas.asu.edu/belief-search

  17. Questions?

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