1. Eyal Amir (UC Berkeley) Barbara Engelhardt (UC Berkeley)
Factored Planning
Eyal Amir (UC Berkeley)
Barbara Engelhardt (UC Berkeley)
Basic goal. – state in page 2
Factored Planning

2. Motivation Planning in structured domains
Scale up planners to large domains
Avoid backtracking of search for plans
Techniques: Similar to structured exact logical and probabilistic reasoning
(Pearl’88), (Dechter & Rish’94), (Amir & McIlraith ’00,’01), (McCartney etal. ’03)
Factored Planning

3. Talk Outline Factored domains Factored planning algorithm
Decomposition algorithm
Factored Planning

4. Example Planning Domain
Room 1
(20 windows)
Room 2
(20 windows)
Fluents: closed(x), done1, done2, at1, at2
Actions: close(x), move-R, move-L
Goal: done1,done2 (all windows closed)
Initial state: at2
Factored Planning

5. Example Planning Domain
move-left
2. close(1), close(2), …
3. move-right
close(21), close(22), …
Fluents: closed(x), done1, done2, at1, at2
Actions: close(x), move-R, move-L
Goal: done1,done2 (all windows closed)
Initial state: at2
Factored Planning

6. Example Planning Domain
Room 1
(20 windows)
Room 2
(20 windows)
at2
Fluents: closed(x), done1, done2, at1, at2
Actions: close(x), move-R, move-L
Goal: done1,done2 (all windows closed)
Initial state: at2
Factored Planning

7. Example Planning Domain
Room 1
(20 windows)
Room 2
(20 windows)
at2
Fluents: closed(x), done1, done2, at1, at2
Actions: close(x), move-R, move-L
Goal: done1,done2 (all windows closed)
Initial state: at2
Factored Planning

8. Example Planning Domain
Room 1
(20 windows)
Room 2
(20 windows)
at1
Fluents: closed(x), done1, done2, at1, at2
Actions: close(x), move-R, move-L
Goal: done1,done2 (all windows closed)
Initial state: at2
Factored Planning

9. Example Planning Domain
Room 1
(20 windows)
Room 2
(20 windows)
at1
Fluents: closed(x), done1, done2, at1, at2
Actions: close(x), move-R, move-L
Goal: done1,done2 (all windows closed)
Initial state: at2
Factored Planning

10. Example Planning Domain
Room 1
(20 windows)
Room 2
(20 windows)
at1
Fluents: closed(x), done1, done2, at1, at2
Actions: close(x), move-R, move-L
Goal: done1,done2 (all windows closed)
Initial state: at2
Factored Planning

11. Example Planning Domain
Room 1
(20 windows)
Room 2
(20 windows)
done1
at1
Fluents: closed(x), done1, done2, at1, at2
Actions: close(x), move-R, move-L
Goal: done1,done2 (all windows closed)
Initial state: at2
Factored Planning

12. Example Planning Domain
Room 1
(20 windows)
Room 2
(20 windows)
done1
at1
Fluents: closed(x), done1, done2, at1, at2
Actions: close(x), move-R, move-L
Goal: done1,done2 (all windows closed)
Initial state: at2
Factored Planning

13. Example Planning Domain
Room 1
(20 windows)
Room 2
(20 windows)
done1
at2
Fluents: closed(x), done1, done2, at1, at2
Actions: close(x), move-R, move-L
Goal: done1,done2 (all windows closed)
Initial state: at2
Factored Planning

14. Example Planning Domain
Room 1
(20 windows)
Room 2
(20 windows)
done1
at2
Fluents: closed(x), done1, done2, at1, at2
Actions: close(x), move-R, move-L
Goal: done1,done2 (all windows closed)
Initial state: at2
Factored Planning

15. Example Planning Domain
Room 1
(20 windows)
Room 2
(20 windows)
done1
at2
Fluents: closed(x), done1, done2, at1, at2
Actions: close(x), move-R, move-L
Goal: done1,done2 (all windows closed)
Initial state: at2
Factored Planning

16. Example Planning Domain
Room 1
(20 windows)
Room 2
(20 windows)
done1
done2
at2
Fluents: closed(x), done1, done2, at1, at2
Actions: close(x), move-R, move-L
Goal: done1,done2 (all windows closed)
Initial state: at2
Factored Planning

17. Example Planning Domain
move-left
2. close(1), close(2), …
3. move-right
close(21), close(22), …
Fluents: closed(x), done1, done2, at1, at2
Actions: close(x), move-R, move-L
Goal: done1,done2 (all windows closed)
Initial state: at2
Factored Planning

18. Factored Planning Domain
move-left
2. close(1), close(2), …
3. move-right
close(21), close(22), …
Fluents:
closed(x) (1x20)
done1, at1, at2
Actions:
Close(x) (1x20)
Move-R, move-L
Fluents:
closed(x) (21x40)
done1,done2,at1,at2
Actions:
Close(x) (21x40)
Move-R, move-L
at1,at2
done1
Factored Planning

19. Intuition Planning separately in different parts
Combine separate plans to form complete plan
Difficulty: want a sound + complete procedure that is always applicable
Potential benefits:
Fast planning & replanning
Scaling to very large domains
Factored Planning

20. Talk Outline Factored domains Factored planning algorithm
Decomposition algorithm
Factored Planning

21. Planning via Dynamic Program
Room 1
(20 windows)
Room 2
(20 windows)
Send
Messages
(one way)
Do some
Processing
In subdomain 1
Do some
Processing
In subdomain 2
+ messages
Factored Planning

22. Planning Algorithm (example)
Room 1
(20 windows)
Room 2
(20 windows)
Find capabilities
of subdomain 1
relevant to
subdomain 2
Factored Planning

23. Planning Algorithm (example)
Room 1
“if at1, then there is
a way to make
done1 true”
Room 2
(20 windows)
Find capabilities
of subdomain 1
relevant to
subdomain 2
Factored Planning

24. Planning Algorithm (example)
Room 1
“if at1, then there is
a way to make
done1 true”
Room 2
(20 windows)
Find capabilities
of subdomain 1
Create a new action
In subdomain 2:
relevant to
subdomain 2
“make done1 true”
Precond: at1
Effect: done1
Factored Planning

25. Planning Algorithm (example)
Room 1
“if at1, then there is
a way to make
done1 true”
Room 2
(20 windows)
Find capabilities
of subdomain 1
Find plan in subdomain 2
relevant to
subdomain 2
“make done1 true”
Precond: at1
Effect: done1
Factored Planning

26. Planning Algorithm (example)
Room 2
Room 1
“if at1, then there is
a way to make
done1 true”
Plan:
move-left
“make done1 true”
move-right
close(21),
close(22), …
Find capabilities
of subdomain 1
Find plan in subdomain 2
relevant to
subdomain 2
“make done1 true”
Precond: at1
Effect: done1
Factored Planning

27. Planning Algorithm (example)
Room 2
Room 1
“if at1, then there is
a way to make
done1 true”
Plan:
move-left
“make done1 true”
move-right
close(21),
close(22), …
Find capabilities
of subdomain 1
Expand plan to
Include only atomic
actions
relevant to
subdomain 2
Factored Planning

28. Planning Algorithm (example)
Room 2
Room 1
“if at1, then there is
a way to make
done1 true”
Plan:
move-left
A. close(1),
B. close(2), …
3. move-right
close(21),
close(22), …
Find capabilities
of subdomain 1
Expand plan to
Include only atomic
actions
relevant to
subdomain 2
Factored Planning

29. Summary & Outlook So far: example of algorithm
Next: algorithm + generalization
Separator
Fluents:
closed(x) (0<x<21)
done1, at1, at2
Actions:
Close(x) (0<x<21)
Move-R, move-L
closed(x) (19<x<41)
done1,done2,at1,at2
Close(x) (19<x<41)
at1,at2
done1
Factored Planning

30. Planning Algorithm (2 partitions)
INPUT: 2 Partitions of fluents and actions
Initial state, Goal condition
Iterate over values V for separator:
A. Find achievable goals for part 1 from V
B. Send found plans to part 2
Add new actions for plans of part 1
Find plan for goal in part 2
Replace new actions with atomic ones
Factored Planning

31. General Messages Room 1 “if at1, then there is a way to make
done1 true”
Room 2
(20 windows)
power
Not true anymore
What if we need more interactions between rooms?
Example: robot must recharge batteries
Factored Planning

32. General Messages Room 1 Room 2 “if at1, and when (20 windows)
needed battery_ok,
then we can make
done1 true”
Room 2
(20 windows)
power
What if we need more interactions between rooms?
Example: robot must recharge batteries
Factored Planning

33. Planning Algorithm INPUT: m Partitions of fluents and actions
Initial state, Goal condition
Factored Planning

34. Planning Algorithm INPUT: m Partitions of fluents and actions
Initial state, Goal condition
Factored Planning

35. Planning Algorithm INPUT: m Partitions of fluents and actions
Initial state, Goal condition
Factored Planning

36. Planning Algorithm INPUT: m Partitions of fluents and actions
Initial state, Goal condition
Factored Planning

37. Planning Algorithm INPUT: m Partitions of fluents and actions
Initial state, Goal condition
Factored Planning

38. Planning Algorithm INPUT: m Partitions of fluents and actions
Initial state, Goal condition
Factored Planning

39. Planning Algorithm INPUT: m Partitions of fluents and actions
Initial state, Goal condition
Factored Planning

40. Planning Algorithm INPUT: m Partitions of fluents and actions
Initial state, Goal condition
Factored Planning

41. Planning Algorithm INPUT: m Partitions of fluents and actions
Initial state, Goal condition
Factored Planning

42. Planning Algorithm INPUT: m Partitions of fluents and actions
Initial state, Goal condition
Factored Planning

43. Planning Algorithm INPUT: m Partitions of fluents and actions
Initial state, Goal condition
Factored Planning

44. Planning Algorithm INPUT: m Partitions of fluents and actions
Initial state, Goal condition
Find plan in final partition
Replace new actions
with atomic actions
Factored Planning

45. Analysis of Algorithm
Theorem: Planning algorithm is sound and complete.
Theorem: Algorithm runs in time
O(m • 2k1•k2)
m = number of partitions
k1 = # fluents in largest partition
k2 = “plan width”:
# back-and-forth interactions
between partitions in a plan
Factored Planning

46. Analysis of Algorithm
Theorem: Planning algorithm is sound and complete.
Theorem: Algorithm runs in time
O(m • 2k1•k2)
Two Rooms Example:
m = 2 k1 = 24 k2 = 1
Factored planning: O(2 • 224)
Traditional planning: O(244)
Factored Planning

47. Experiment: Ring of Rooms
Time (in milliseconds)
Number of rooms
Factored Planning

48. Talk Outline Factored domains Factored planning algorithm
Decomposition algorithm
Factored Planning

49. Decomposition Algorithm
Convert into a graph problem
Find a tree decomposition of low width
Decompose the problem using tree
Factored Planning

50. Decomposition Algorithm
1. Convert into a graph problem
closed(1)
close(1)
close(21)
closed(21)
closed(2)
close(2)
close(22)
closed(22)
done1
move-R
done2
move-L
at1
at2
Factored Planning

51. Decomposition Algorithm
1. Convert into a graph problem
closed(1)
close(1)
close(21)
closed(21)
closed(2)
close(2)
close(22)
closed(22)
done1
move-R
done2
move-L
at1
at2
Factored Planning

52. Decomposition Algorithm
1. Convert into a graph problem
closed(1)
close(1)
close(21)
closed(21)
closed(2)
close(2)
close(22)
closed(22)
done1
move-R
done2
move-L
at1
at2
Factored Planning

53. Decomposition Algorithm
1. Convert into a graph problem
closed(1)
close(1)
close(21)
closed(21)
closed(2)
close(2)
close(22)
closed(22)
done1
move-R
done2
move-L
at1
at2
Factored Planning

54. Decomposition Algorithm
2. Find a tree decomposition of low width
closed(1)
close(1)
close(21)
closed(21)
closed(2)
close(2)
close(22)
closed(22)
done1
move-R
done2
move-L
at1
at2
Factored Planning

55. Decomposition Algorithm
2. Find a tree decomposition of low width
closed(1)
close(1)
close(21)
closed(21)
closed(2)
close(2)
close(22)
closed(22)
done1
move-R
done2
move-L
at1
at2
Factored Planning

56. Decomposition Algorithm
3. Decompose planning problem accordingly
closed(1)
close(1)
close(21)
closed(21)
closed(2)
close(2)
close(22)
closed(22)
done1
move-R
done2
move-L
at1
at2
Factored Planning

57. Decomposition Algorithm
3. Decompose planning problem accordingly
done1
Fluents:
closed(x) (0<x<21)
done1, at1, at2
Actions:
Close(x) (0<x<21)
Move-R, move-L
Fluents:
closed(x) (19<x<41)
done1,done2,at1,at2
Actions:
Close(x) (19<x<41)
Move-R, move-L
at1
at2
Factored Planning

58. Decomposition Algorithm
3. Decompose planning problem accordingly
Room 1
(20 windows)
Room 2
(20 windows)
Factored Planning

59. Decomposition Algorithm
Convert into a graph problem
Find a tree decomposition of low width
Can be done using known algorithms (e.g., (Rose ’76), (Amir 2001))
Decompose the problem using tree
Factored Planning

60. Conclusions Factored planning algorithm
Decomposition algorithm relies on known graph algorithms
Algorithm applicable to all domains
Always sound and complete (unlike (Guestrin etal. ’01) - MDPs)
Tractability of algorithm depends on quality of domain decomposition and decomposition properties of solution
Factored Planning

61. Applications & Future Work
Nondeterministic domains
Stochastic domains
First-order decompositions
Automatic generation of subsumption architectures
Factored Planning

62. THE END
Factored Planning

63. Related Works
Factored reasoning [Pearl’88], [Amir & McIlraith’00,’01], [MacCartney etal.’03]
Structured planning: Hierarchical planning, structured planning [Lanskey & Getoor ’95], Agents [Lansky’91], …
Stochastic planning: [Parr’99], [Guestrin etal. ’01]
Factored Planning

64. Factored Planning