Structural Symmetries of the Lifted Representation of Classical - - PowerPoint PPT Presentation

▶

structural symmetries of the lifted representation of

Structural Symmetries of the Lifted Representation of Classical - - PowerPoint PPT Presentation

Sep 16, 2023 38 likes •289 views

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis Structural Symmetries of the Lifted Representation of Classical Planning Tasks Silvan Sievers 1 Gabriele Rger 1 Martin Wehrle 1 Michael Katz 2 1 University of Basel,

slide-1

SLIDE 1

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Structural Symmetries of the Lifted Representation of Classical Planning Tasks

Silvan Sievers1 Gabriele Röger1 Martin Wehrle1 Michael Katz2

1University of Basel, Switzerland 2IBM Watson Health, Haifa, Israel

June 20, 2017

slide-2

SLIDE 2

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Motivation

Recent interest in symmetries for planning:

Structural symmetries for ground (STRIPS) planning tasks E.g. symmetry-based pruning in forward search

slide-3

SLIDE 3

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Motivation

Recent interest in symmetries for planning:

Structural symmetries for ground (STRIPS) planning tasks E.g. symmetry-based pruning in forward search

In this work:

Reason about symmetries on lifted planning tasks Provide the foundation for using structural symmetries for applications prior grounding

slide-4

SLIDE 4

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Outline

1

Structural Symmetries

2

Grounding

3

Relation to STRIPS

4

Quantitative Analysis

slide-5

SLIDE 5

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Abstract Structures

S: set of symbols s with type t(s) Inductive definition of abstract structures:

s ∈ S abstract structure If A1, . . . , An abstract structures, then also A1, . . . , An and {A1, . . . , An} abstract structures

slide-6

SLIDE 6

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Structural Symmetries

Symbol mapping σ: permutation of S with t(σ(s)) = t(s) Induced abstract structure mapping ˜ σ: ˜ σ(A) :=      σ(A) if A ∈ S {˜ σ(A1), . . . , ˜ σ(An)} if A = {A1, . . . , An} ˜ σ(A1), . . . , ˜ σ(An) if A = A1, . . . , An σ structural symmetry for abstract structure A if ˜ σ(A) = A

slide-7

SLIDE 7

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Lifted Planning Tasks as Abstract Structures

Lifted representation: normalized PDDL with action costs Lifted planning task Π as abstract structure:

Components such as objects, variables, predicates etc: symbols Atoms, literals, function terms, operators, axioms etc: composed abstract structures

slide-8

SLIDE 8

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Example Planning Task

bob shed middle gate

slide-9

SLIDE 9

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Example Planning Task

bob shed middle gate

Two symmetries on the lifted representation: nuts/spanners

slide-10

SLIDE 10

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Outline

1

Structural Symmetries

2

Grounding

3

Relation to STRIPS

4

Quantitative Analysis

slide-11

SLIDE 11

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Full Grounding

ground(Π): fully grounded planning task Π

slide-12

SLIDE 12

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Full Grounding

ground(Π): fully grounded planning task Π Theorem If σ is a structural symmetry for planning task Π, then σ is a structural symmetry for ground(Π).

slide-13

SLIDE 13

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Optimized Grounding

Full grounding infeasible in practice Optimized grounding (groundopt(Π)): remove some irrelevant part of the task representation

slide-14

SLIDE 14

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Optimized Grounding

Full grounding infeasible in practice Optimized grounding (groundopt(Π)): remove some irrelevant part of the task representation Observation If σ is a structural symmetry for planning task Π, then σ is not necessarily a structural symmetry for groundopt(Π).

slide-15

SLIDE 15

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Optimized Grounding

Full grounding infeasible in practice Optimized grounding (groundopt(Π)): remove some irrelevant part of the task representation Observation If σ is a structural symmetry for planning task Π, then σ is not necessarily a structural symmetry for groundopt(Π).

bob shed middle gate

slide-16

SLIDE 16

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Rational Grounding

Optimized grounding unreasonable assumption Rational grounding (groundrat(Π)): remove all or no symmetric irrelevant parts

slide-17

SLIDE 17

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Rational Grounding

Optimized grounding unreasonable assumption Rational grounding (groundrat(Π)): remove all or no symmetric irrelevant parts Theorem If σ is a structural symmetry for planning task Π, then σ is a structural symmetry for groundrat(Π).

slide-18

SLIDE 18

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Outline

1

Structural Symmetries

2

Grounding

3

Relation to STRIPS

4

Quantitative Analysis

slide-19

SLIDE 19

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Relation to STRIPS Representations

Propositional STRIPS tasks: set of symbols contains atoms

slide-20

SLIDE 20

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Relation to STRIPS Representations

Propositional STRIPS tasks: set of symbols contains atoms Representational differences:

Example symmetry of STRIPS task Π: σ(P(a)) = P(a) and σ(P(b)) = Q(b) No analogous symmetry for AΠ: cannot map predicate P to both Q and P

slide-21

SLIDE 21

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Relation to STRIPS Representations

Propositional STRIPS tasks: set of symbols contains atoms Representational differences:

Example symmetry of STRIPS task Π: σ(P(a)) = P(a) and σ(P(b)) = Q(b) No analogous symmetry for AΠ: cannot map predicate P to both Q and P

Other direction:

If σ symmetry of ground task Π (in our definition), then σ also symmetry of Π (in STRIPS) If σ symmetry of lifted task Π, then σ also transition graph symmetry

slide-22

SLIDE 22

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Outline

1

Structural Symmetries

2

Grounding

3

Relation to STRIPS

4

Quantitative Analysis

slide-23

SLIDE 23

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Summarized Results

Computation of symmetries as graph automorphisms 2518 in 77 domains (all sequential track IPC benchmarks) Only 9 domains without symmetries and 26 domains with majority of no symmetries 1430 of 2518 with symmetries Cheap to compute with one exception (ground task)

slide-24

SLIDE 24

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Dicussion

Summary:

Structural symmetries of the lifted representation Lifted symmetries also symmetries of ground representations Benchmarks: many symmetries of the lifted representation

slide-25

SLIDE 25

Structural Symmetries Grounding Relation to STRIPS Quantitative Analysis

Dicussion

Summary:

Structural symmetries of the lifted representation Lifted symmetries also symmetries of ground representations Benchmarks: many symmetries of the lifted representation

Future work:

Accelerated computation of invariants/grounding: consider

nly subset of (symmetric) objects

State space reformulations