Correlation Complexity of Classical Planning Domains Jendrik Seipp - - PowerPoint PPT Presentation

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Correlation Complexity of Classical Planning Domains Jendrik Seipp - - PowerPoint PPT Presentation

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Correlation Complexity of Classical Planning Domains Jendrik Seipp Florian Pommerening Gabriele R oger Malte Helmert University of Basel June 13, 2016 J. Seipp, F. Pommerening, G. R oger, M. Helmert (Basel) Correlation Complexity

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SLIDE 1

Correlation Complexity

  • f Classical Planning Domains

Jendrik Seipp Florian Pommerening Gabriele R¨

  • ger

Malte Helmert

University of Basel

June 13, 2016

  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Some Planning Tasks are Easy

  • Domain independent planning is (PSPACE) hard.
  • But some domains are easy.
  • How can we quantify this?

A B

  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Related Concepts

Width

  • (macro-)persistent Hamming width

(Chen and Gim´ enez, 2007; 2009)

  • serialized iterated width

(Lipovetzky and Geffner, 2012; 2014) Search space topology

  • Fixing the heuristic, how do search algorithms behave

(Hoffmann, 2005) Our approach

  • Fixing the behavior of search algorithms,

how complex does the heuristic need to be?

  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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SLIDE 4

Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Main Question

How complex must a heuristic be to guide a forward search directly to the goal?

  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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SLIDE 5

Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Main Question

How complex must a heuristic be to guide a forward search directly to the goal?

  • What does “guide directly to the goal” mean?
  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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SLIDE 6

Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Main Question

How complex must a heuristic be to guide a forward search directly to the goal?

  • What does “guide directly to the goal” mean?
  • How can we measure the complexity of a heuristic?
  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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SLIDE 7

Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Main Question

How complex must a heuristic be to guide a forward search directly to the goal?

  • What does “guide directly to the goal” mean?
  • How can we measure the complexity of a heuristic?
  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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SLIDE 8

Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Heuristic Properties

  • alive state: reachable + solvable + non-goal
  • descending: all alive states have an improving successor
  • dead-end avoiding: all improving successors of alive states are

solvable

8 10 4 7 9

  • 6

11

  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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SLIDE 9

Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Main Question

How complex must a heuristic be to guide a forward search directly to the goal?

  • What does “guide directly to the goal” mean?

→ descending and dead-end avoiding

  • How can we measure the complexity of a heuristic?
  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

slide-10
SLIDE 10

Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Main Question

How complex must a heuristic be to guide a forward search directly to the goal?

  • What does “guide directly to the goal” mean?

→ descending and dead-end avoiding

  • How can we measure the complexity of a heuristic?
  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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SLIDE 11

Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Potential Heuristics

States factored into facts Features: conjunction of facts Weights for features w

  • A
  • = 8; w

 

B

  = 1; w ( ) = 4 Heuristic value h  

A B

  = 8 + 8 + 1 + 4 = 21

  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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SLIDE 12

Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Potential Heuristics

States factored into facts Features: conjunction of facts Weights for features w

  • A
  • = 8; w

 

B

  = 1; w ( ) = 4 ; w  

B

  = −2 Heuristic value h  

A B

  = 8 + 8 + 1 + 4 − 2 = 19

  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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SLIDE 13

Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Potential Heuristics

States factored into facts Features: conjunction of facts Weights for features w

  • A
  • = 8; w

 

B

  = 1; w ( ) = 4 ; w  

B

  = −2 Heuristic value h  

A B

  = 8 + 8 + 1 + 4 − 2 = 19 Dimension: number of facts in largest feature

  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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SLIDE 14

Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Main Question

How complex must a heuristic be to guide a forward search directly to the goal?

  • What does “guide directly to the goal” mean?

→ descending and dead-end avoiding

  • How can we measure the complexity of a heuristic?
  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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SLIDE 15

Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Main Question

How complex must a heuristic be to guide a forward search directly to the goal?

  • What does “guide directly to the goal” mean?

→ descending and dead-end avoiding

  • How can we measure the complexity of a heuristic?

→ dimension of potential heuristics

  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Correlation Complexity

Definition (correlation complexity of a planning task) minimum dimension of a descending, dead-end avoiding potential heuristic for the task Definition (correlation complexity of a planning domain) maximal correlation complexity of all tasks in the domain

  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Correlation Complexity of Some Domains

Correlation Complexity 2

  • Blocksworld without an arm
  • Gripper
  • Spanner
  • VisitAll

Correlation Complexity 3

000 001 010 011 100 101 110 111

Construction based on 3-bit Gray code

  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Conclusion and Future Work

  • New measure for the complexity of classical planning tasks.
  • Measures how interrelated the task’s variables are.
  • All studied benchmark domains have correlation complexity 2.
  • Next: find good features and weights automatically.
  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Extra Slides

  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Gripper has Correlation Complexity 2

Weight Function w(r-in-B) = 1 w(b-in-A) = 8 w(b-in-G) = 4 w(r-in-B ∧ b-in-G) = −2

  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Pick-up-in-A

w(r-in-B) = 1, w(b-in-A) = 8, w(b-in-G) = 4, w(r-in-B ∧ b-in-G) = −2

A B

adds: b-in-G removes: b-in-A difference: + 4 − 8 = −4

  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Move-to-B

w(r-in-B) = 1, w(b-in-A) = 8, w(b-in-G) = 4, w(r-in-B ∧ b-in-G) = −2

A B

adds: r-in-B, r-in-B ∧ b-in-G removes: — difference: + 1 + (−2) = −1

  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Drop-in-B

w(r-in-B) = 1, w(b-in-A) = 8, w(b-in-G) = 4, w(r-in-B ∧ b-in-G) = −2

A B

adds: — removes: b-in-G, r-in-B ∧ b-in-G difference: − 4 − (−2) = −2

  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Move-to-A

w(r-in-B) = 1, w(b-in-A) = 8, w(b-in-G) = 4, w(r-in-B ∧ b-in-G) = −2

A B

adds: — removes: r-in-B difference: −1

  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity

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Descending, Dead-end Avoiding Heuristics Heuristic Complexity Correlation Complexity Results Example

Example Task with Correlation Complexity 3

  • 3-bit Gray code:

000 001 010 011 100 101 110 111

  • J. Seipp, F. Pommerening, G. R¨
  • ger, M. Helmert (Basel)

Correlation Complexity