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Transcript of Top 5 Worst Times For A Conference Talk 1.Last Day 2.Last Session of Last Day 3.Last Talk 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
Heuristic Guidance Measures For Conformant Planning
Daniel Bryce & Subbarao KambhampatiDept of Computer Science & Engineering
Arizona State University
ICAPS-04
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!!!
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)
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
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
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
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 …
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
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
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
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
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
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
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
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
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
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
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)