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Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk of Last Session of Last Day 4.Last Talk of Last Session of Last Day, after Best Paper Award 5.Last Talk of Last Session of Last Day, after Best Paper Award on Same Topic

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Page 1: Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk of Last Session of Last Day 4.Last Talk of Last Session of Last

Top 5 Worst Times For A Conference Talk

1. Last Day

2. Last Session of Last Day

3. Last Talk of Last Session of Last Day

4. Last Talk of Last Session of Last Day, after Best Paper Award

5. Last Talk of Last Session of Last Day, after Best Paper Award on Same Topic

Page 2: Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk of Last Session of Last Day 4.Last Talk of Last Session of Last

Heuristic Guidance Measures For Conformant Planning

Daniel Bryce & Subbarao KambhampatiDept of Computer Science & Engineering

Arizona State University

ICAPS-04

Page 3: Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk of Last Session of Last Day 4.Last Talk of Last Session of Last

Talk Outline

• Contributions• Search • Heuristic Computation

– Single, Unioned Graph– Multiple Graphs– Single, Labeled Graph

• System Architecture• Empirical Results• Applications to Contingent Planning!!!• Conclusion & Future Work

– Applications to Stochastic Planning!!!

Page 4: Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk of Last Session of Last Day 4.Last Talk of Last Session of Last

Contributions

• What should belief space search distance estimates measure? – Previous approaches to heuristics do not reflect

true nature of distances in belief space planning• Cardinality: MBP planners• State to State plans: GPT planner• State to State plan overlap

• How do we compute these measures efficiently? – (Concentration of Talk)

Page 5: Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk of Last Session of Last Day 4.Last Talk of Last Session of Last

Search

• Belief States represented as formulas– Belief State contains all states consistent with the

formula– Use Conjunctive Normal Form

• Actions have (Un)Conditional Effects and Enabling Preconditions– All conditions and effects are formulas

• Disjunctive Preconditions and Non-deterministic Effects

• A* Regression Search in Belief Space – Terminates when Initial Belief State Entails the Search

Belief State

Page 6: Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk of Last Session of Last Day 4.Last Talk of Last Session of Last

Planning Graph Heuristic Computation

• Heuristics – BFS

– Cardinality

– Max, Sum, Level, Relaxed Plans

• Planning Graph Structures– Single, unioned planning graph (SG)

– Multiple, independent planning graphs (MG)

– Single, labeled planning graph (LUG) • [Bryce , et. al, 2004] – AAAI MDP workshop

Page 7: Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk of Last Session of Last Day 4.Last Talk of Last Session of Last

Using a Single, Unioned GraphPM

QM

RM

P

Q

R

M

A1

A2

A3

Q

R

M

K

LA4

GA5

PA1

A2

A3

Q

R

M

K

L

P

G

A4K

A1P

M

Heuristic Estimate = 2

•Not effective•Lose world specific support information

Union literals from all initial states into a conjunctive initial graph level

•Minimal implementation

Page 8: Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk of Last Session of Last Day 4.Last Talk of Last Session of Last

Using Multiple GraphsP

M

A1 P

M

K

A1 P

M

KA4

G

R

MA3

R

M

L

A3R

M

L

GA5

PM

QM

RM

Q

M

A2Q

M

K

A2Q

KA4

G

M

G

A4K

A1

M

P

G

A4K

A2Q

M

GA5

L

A3R

M

•Same-world Mutexes

•Memory Intensive•Heuristic Computation Can be costly

Unioning these graphs a priori would give much savings …

Page 9: Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk of Last Session of Last Day 4.Last Talk of Last Session of Last

Using a Single, Labeled Graph(joint work with David E. Smith)

P

Q

R

A1

A2

A3

P

Q

R

M

L

A1

A2

A3

P

Q

R

L

A5

Action Labels:Conjunction of Labels of Supporting Literals

Literal Labels:Disjunction of LabelsOf Supporting Actions

PM

QM

RM

KA4

G

K

A1

A2

A3

P

Q

R

M

GA5

A4L

K

A1

A2

A3

P

Q

R

M

Heuristic Value = 5

•Memory Efficient•Cheap Heuristics•Scalable•Extensible

Benefits from BDD’s

~Q & ~R

~P & ~R

~P & ~Q

(~P & ~R) V (~Q & ~R)

(~P & ~R) V (~Q & ~R) V(~P & ~Q)

M

True

Label Key

Labels signify possible worldsunder which a literal holds

Page 10: Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk of Last Session of Last Day 4.Last Talk of Last Session of Last

System Architecture

A* Search Engine(HSP-r)

Heuristics

PlanningGraph(s)

(IPP)

BeliefStates

Labels (CUDD)

ModelChecker

(NuSMV)

Off – The - Shelf Custom

IPC PDDL Parser

Sear

ches

Gui

ded

B

y

Input forInput for

Con

dens

e

Validates

Extracted

From

Page 11: Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk of Last Session of Last Day 4.Last Talk of Last Session of Last

Rovers Total Time

100

1000

10000

100000

1000000

1 2 3 4 5 6

Problem

To

tal T

ime

(ms)

0

card

card'

SG-max

SG-sum

SG-level

SG-RP

Rovers Total Time

100

1000

10000

100000

1000000

1 2 3 4 5 6

Problem

To

tal T

ime

(ms)

MG-max

MG-sum

MG-level

MG-RPM

MG-RPU

LUG-max

LUG-sum

LUG-level

LUG-RP

LUG-RP(MUX)

Sum and Relaxed Plan Are Best for a single Graph

Relaxed Plan is Best Multiple Or Label Graphs

Label Graph using mutexesWith relaxed plan is best overall

Page 12: Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk of Last Session of Last Day 4.Last Talk of Last Session of Last

Logistics Total Time

100

1000

10000

100000

1000000

1 2 3 4 5Problem

To

tal T

ime

(m

s)

0

cardcard'

SG-max

SG-sum

SG-levelSG-RP

Logistics Total Time

100

1000

10000

100000

1000000

1 2 3 4 5Problem

To

tal T

ime

(m

s)

MG-max

MG-sum

MG-level

MG-RPM

MG-RPU

LUG-max

LUG-sum

LUG-level

LUG-RP

LUG-RP(MUX)

Relaxed Plan is Best for a single Graph

Sum is Best for Multiple Graphs

Label Graph using mutexesWith relaxed plan is best overall

Page 13: Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk of Last Session of Last Day 4.Last Talk of Last Session of Last

BT Total Time

100

1000

10000

100000

1000000

2 10 20 30 40 50 60 70 80Problem

To

tal T

ime

(m

s)

0

cardcard'

SG-max

SG-sum

SG-levelSG-RP

BT Total Time

100

1000

10000

100000

1000000

2 10 20 30 40 50 60 70 80Problem

To

tal

Tim

e (m

s)

MG-max

MG-sum

MG-level

MG-RPM

MG-RPU

LUG-max

LUG-sum

LUG-level

LUG-RP

LUG-RP(MUX)

Cardinality does well

Multiple Graph Union Relaxed Plan scales

Label Graph Relaxed PlanDoes best

Page 14: Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk of Last Session of Last Day 4.Last Talk of Last Session of Last

Rovers Plan Length

0

10

20

30

40

50

1 2 3 4 5 6

Problem

Pla

n L

eng

th

CAltAlt

KACMBP

HSCP

GPT

CGP

Rovers Total Time

10

100

1000

10000

100000

1000000

1 2 3 4 5 6

Problem

To

tal

Tim

e (m

s)

CAltAlt

KACMBP

HSCP

GPT

CGP

OptimalApproachesscale poorly

Cardinality approaches are fasterBut quality suffers

Relaxed Plan approaches Scale better with time approximate to cardinalityAnd quality comparable to optimal

Page 15: Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk of Last Session of Last Day 4.Last Talk of Last Session of Last

Logistics Total Time

10

100

1000

10000

100000

1000000

1 2 3 4 5

Problem

To

tal T

ime

(m

s)

CAltAlt

KACMBP

HSCP

GPT

CGP

Logistics Plan Length

051015202530354045

1 2 3 4 5Problem

Pla

n L

eng

th

CAltAlt

KACMBP

HSCP

GPT

CGP

OptimalApproachesscale poorly

Cardinality approaches are fasterBut quality suffers

Relaxed Plan approaches Scale better with time approximate to cardinalityAnd quality comparable to optimal

Page 16: Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk of Last Session of Last Day 4.Last Talk of Last Session of Last

Contingent Planning

• Progression Planner – PBSP– LAO* type search -- Non-Deterministic &

Partially Observable– Build Planning Graph to compute heuristic for

each Belief State• No Mutexes Computed

• Added Observational Actions to Domains

Page 17: Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk of Last Session of Last Day 4.Last Talk of Last Session of Last

Contingent Logistics Total Time

1

10

100

1000

10000

100000

1 2 3 4 5

Problem

To

tal T

ime

(m

s)

PBSP

MBP

GPT

SGP

Contingent Logistics Max Branch Length

1

10

100

1000

10000

1 2 3 4 5

Problem

Pla

n L

en

gth PBSP

MBP

GPT

SGP

OptimalApproachesscale poorly

Cardinality approaches are fasterAnd scale better But quality suffers by two orders of magnitude

Relaxed Plan approaches Scale better than optimal approaches and have Comparable quality

Page 18: Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk of Last Session of Last Day 4.Last Talk of Last Session of Last

Conclusions & Future Work

• Conclusion– Distance Estimations using “overlap” are more informed than cardinality

and max state to state heuristics– Multiple Planning Graphs give good heuristics, but are costly

• Labeled Planning graphs reduce cost– Planning Graph Heuristics help control plan length while scaling to

difficult problems• More details in:

– TR at: http://rakaposhi.eas.asu.edu/belief-search• Conformant, Contingent – all planning graph types

– AAAI-04 MDP workshop• Labeled Planning Graph for conformant planning

• Future Work – Stochastic Planning

Page 19: Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk of Last Session of Last Day 4.Last Talk of Last Session of Last

Stochastic PlanningStochasticPlanningProblem

Non-DeterministicPlanner

(PBSP or CAltAlt)

DeterministicPlanner

(UCPOP)

New Approach Buridan

SeedStochastic

Plan

Relaxation Of Instance

ConvertSolution to Stochastic

PlanDeterministic

PlanNon-

DeterministicPlan

Stochastic Plan

Local Search

To ImproveProbability of

Satisfaction

A seed non-deterministicplan is likely to reflect physics of a stochastic planning problem better than a seed deterministic plan.

Can use RelaxedPlans that are greedyOn Probability byUsing Probability in Planning Graph (similar to PGraphPlan)