Top 5 Worst Times For A Conference Talk

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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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Heuristic Guidance Measures For Conformant
Planning

• Daniel Bryce Subbarao Kambhampati
• Dept of Computer Science Engineering
• Arizona State University
• ICAPS-04

3
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!!!

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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)

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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

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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

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Using a Single, Unioned Graph
P
P
P
P
P
M
A1
A1
A1
Q
Q
Q
Q

• Minimal
• implementation

A2
A2
M
R
R
R
R
A3
A3
M
M
M

• Not effective
• Lose world specific support information

M
M
K
K
K
Heuristic Estimate 2
A4
A4
L
L
Union literals from all initial states into a
conjunctive initial graph level
A5
G
G
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Using Multiple Graphs
P
P
P
P
A1
A1
A1

• Same-world Mutexes

M
M
M
M
P
K
K
K
A4
A4
M
G
G

• Memory Intensive
• Heuristic Computation Can be costly

Q
Q
Q
Q
Q
A2
A2
A2
M
M
M
M
M
R
K
K
K
A4
A4
M
G
G
R
R
R
R
A3
A3
A3
M
M
M
M
L
L
L
A5
A5
G
G
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Using a Single, Labeled Graph(joint work with
David E. Smith)
Action Labels Conjunction of Labels of
Supporting Literals
Labels signify possible worlds under which a
literal holds
P
P
P
P
P
P
M

• Memory Efficient
• Cheap Heuristics
• Scalable
• Extensible

A1
A1
A1
A1
Q
Q
Q
Q
Q
Q
A2
A2
A2
A2
M
R
R
R
R
R
A3
A3
A3
A3
R
M
M
M
M
M
Literal Labels Disjunction of Labels Of
Supporting Actions
K
K
K
Benefits from BDDs
A4
A4
L
L
L
Label Key
True
A5
A5
G
G
(P R) V (Q R)
Q R
P R
(P R) V (Q R) V (P Q)
Heuristic Value 5
P Q
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System Architecture
CAltAlt
IPC PDDL Parser
Input for
Input for
Heuristics
A Search Engine (HSP-r)
Planning Graph(s) (IPP)
Extracted From
Condense
Searches
Labels (CUDD)
Model Checker (NuSMV)
Belief States
Guided By
Validates
Off The - Shelf
Custom
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Sum and Relaxed Plan Are Best for a single Graph
Relaxed Plan is Best Multiple Or Label Graphs
Label Graph using mutexes With relaxed plan is
best overall
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Relaxed Plan is Best for a single Graph
Sum is Best for Multiple Graphs
Label Graph using mutexes With relaxed plan is
best overall
13
Cardinality does well
Multiple Graph Union Relaxed Plan scales
Label Graph Relaxed Plan Does best
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Relaxed Plan approaches Scale better with time
approximate to cardinality And quality comparable
to optimal
OptimalApproaches scale poorly
Cardinality approaches are faster But quality
suffers
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Relaxed Plan approaches Scale better with time
approximate to cardinality And quality comparable
to optimal
OptimalApproaches scale poorly
Cardinality approaches are faster But quality
suffers
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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

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Relaxed Plan approaches Scale better than
optimal approaches and have Comparable quality
OptimalApproaches scale poorly
Cardinality approaches are faster And scale
better But quality suffers by two orders of
magnitude
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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

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Stochastic Planning
Stochastic Planning Problem
New Approach
Buridan
Relaxation Of Instance
Can use Relaxed Plans that are greedy On
Probability by Using Probability in Planning
Graph (similar to PGraphPlan)
Deterministic Planner (UCPOP)
Non-Deterministic Planner (PBSP or CAltAlt)
Convert Solution to Stochastic Plan
Non- DeterministicPlan
Deterministic Plan
Seed Stochastic Plan
A seed non-deterministic plan is likely to
reflect physics of a stochastic planning problem
better than a seed deterministic plan.
Local Search To Improve Probability of
Satisfaction
Stochastic Plan
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Regression Search Example
Actions A1 M P gt K A2 M Q gt
K A3 M R gt L A4 K gt G A5 L gt G
G
A4
G or K must be true before A4 For G to be true
after A4
(G V K)
A5
(G V K V L)
A1
(G V K V L V P) M
Enabling precondition Must be true before A1 was
applied
A2
(G V K V L V P V Q) M
Initially (P V Q V R) (P V Q) (P V R)
(Q V R) M
Initially (P V Q V R) (P V Q) (P V R)
(Q V R) M
A3
Each Clause is Satisfied by a Clause in the
Initial Clausal State -- Done! (5 actions)
(G V K V L V P V Q V R) M
(G V K V L V P V Q V R) M
Goal State G
Clausal States compactly represent disjunction to
sets of uncertain literals Yet, still need
heuristics for the search
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Distance Estimates
Cardinality
Max State to State
State to State Overlap Belief state to Belief
state
4
7
10
2
3
max
union
6
7
min
min
min
5
4
?
3
4
7
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Cardinality does well
Multiple Graph Union Relaxed Plan scales
Label Graph Relaxed Plan Does best, mutexes do
help
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Relaxed Plan approaches Scale better than
optimal approaches, but have quality comparable
to optimal
OptimalApproaches scale poorly
Cardinality approaches are faster And scale
better But quality suffers by an order of
magnitude