1. Problem Solving Agents

2. So Far… Traditional AI begins with some simple premises:
An intelligent agent lives in a particular environment.
An intelligent agent has goals that it wants to achieve.
The environment in which an agent is expected to operate has a large effect on what sort of behaviors it will need and what we should expect it to be able to do.

3. Chapter 3 : Problem Solving by Searching
“In which we see how an agent can find a sequence of actions that achieves its goals when no single action will do.”
Such agents must be able to:
Formulate a goal
Formulate the overall problem
Find a solution

4. Last time I gave you this problem
Three missionaries and three cannibals
Want to cross a river using one canoe.
Canoe can hold up to two people.
Can never be more cannibals than missionaries on either side of the river.
Aim: To get all safely across the river without any missionaries being eaten.

5. Problem Solving Agents
Formulate goal:
get everyone across the river
Formulate problem:
states: various combinations of people on either side of the river
actions: take the canoe (with some people) across the river
restrictions: certain combinations of people are “illegal”
Find solution:
sequence of canoe trips that get everybody (safely) across the river

6. Last time I gave you this problem
Five missionaries and five cannibals
Want to cross a river using one canoe.
Canoe can hold up to three people.
Can never be more cannibals than missionaries on either side of the river.
Aim: To get all safely across the river without any missionaries being eaten.

7. Problem Solving Agents
Example: Traveling in Romania
On holiday in Romania; currently in Arad. Flight leaves tomorrow from Bucharest

8. Problem Solving Agents
Example: Traveling in Romania
On holiday in Romania; currently in Arad. Flight leaves tomorrow from Bucharest Formulate goal: be in Bucharest Formulate problem: states: various cities actions: drive between cities Find solution: sequence of cities, e.g., Arad, Sibiu, Fagaras, Bucharest

9. Problem Solving Agents
Formulate goal:
get the set of rooms clean
Formulate problem:
states: various combinations of dirt and vacuum location
actions: right, left, suck, no-op
Find solution:
sequence of actions that cause all rooms to be clean

10. Appropriate environment for Searching Agents
Observable??
Deterministic??
Episodic??
Static??
Discrete??
Agents??
Yes
Either

11. Problem Types Deterministic, fully observable  single-state problem
Agent knows exactly which state it will be in
Solution is a sequence
Non-observable  conformant problem
Agent may have no idea where it is
Solution (if any) is a sequence
Nondeterministic and/or partially observable  contingency problem
percepts provide new information about current state
solution is a tree or policy
often interleave search, execution
Unknown state space  exploration problem ( “online” )

12. Problem Types Example: vacuum world Start in #5. Solution??
[Right, Suck]

13. Problem Types Deterministic, fully observable  single-state problem
Agent knows exactly which state it will be in
Solution is a sequence
Non-observable  conformant problem
Agent may have no idea where it is
Solution (if any) is a sequence
Nondeterministic and/or partially observable  contingency problem
percepts provide new information about current state
solution is a tree or policy
often interleave search, execution
Unknown state space  exploration problem ( “online” )

14. Problem Types
Conformant, start in {1,2,3,4,5,6,7,8} Solution??

15. Problem Types Conformant, start in {1,2,3,4,5,6,7,8}
e.g., Right goes to {2,4,6,8}.
[Right, Suck, Left, Suck]

16. Problem Types Deterministic, fully observable  single-state problem
Agent knows exactly which state it will be in
Solution is a sequence
Non-observable  conformant problem
Agent may have no idea where it is
Solution (if any) is a sequence
Nondeterministic and/or partially observable  contingency problem
percepts provide new information about current state
solution is a tree or policy
often interleave search, execution
Unknown state space  exploration problem ( “online” )

17. Problem Types Contingency, start in #5
Murphy’s Law: Suck can dirty a clean carpet
Local Sensing: dirt, location only.
Solution??
[Right, if dirt then Suck]

18. Problem Types Deterministic, fully observable  single-state problem
Agent knows exactly which state it will be in
Solution is a sequence
Non-observable  conformant problem
Agent may have no idea where it is
Solution (if any) is a sequence
Nondeterministic and/or partially observable  contingency problem
percepts provide new information about current state
solution is a tree or policy
often interleave search, execution
Unknown state space  exploration problem
“online” search

19. Single-State Problem Formulation
For the time being, we are only interested in the single-state problem formulation
A problem is defined by four items:
initial state e.g., “at Arad”
successor function S(x) = set of action-state pairs e.g., S(Arad) = { <Arad  Zerind, Zerind>, …}
goal test, can be explicit, e.g., x = “at Bucharest” implicit, e.g., NoDirt(x)
path cost (additive) e.g., sum of distances, number of actions executed, etc. C(x,a,y) is the step cost, assumed to be  0

20. Single-State Problem Formulation
A solution is a sequence of actions leading from the initial state to a goal state

21. Problem Formulation Example: vacuum cleaner world state space graph
States?? Actions?? Goal test?? Path cost??

22. Problem Formulation
States?? Integer dirt and robot locations (ignore dirt amounts)
Actions?? Left, Right, Suck, NoOp
Goal test?? No dirt
Path cost?? 1 per action (0 for NoOp)

23. Example: the 8-puzzle
States?? Actions?? Goal test?? Path cost??

24. Example: The 8-puzzle
States?? 9!/2 integer locations of tiles (ignore intermediate positions)
Actions?? Move blank left, right, up, down
Goal test?? = goal state (given)
Path cost?? 1 per move
Note: optimal solution of n-Puzzle family is NP-hard (although 8-Puzzle is NP-complete)

25. Why do we look at “toy” problems.
Real world is absurdly complex state space must be abstracted for problem solving
(Abstract) state = set of real states (Abstract) action = complex combination of real actions e.g., “Arad  Zerind” represents a complex set of possible route, detours, rest stops, etc. For guaranteed realizability, any real state “in Arad” must get to some real state “in Zerind”
(Abstract) solution = set of real paths that are solutions in the real world each abstract action should e “easier” than the original problem!

27. Last time I gave you this problem
Three missionaries and three cannibals
Want to cross a river using one canoe.
Canoe can hold up to two people.
Can never be more cannibals than missionaries on either side of the river.
Aim: To get all safely across the river without any missionaries being eaten.

28. Original Problem Solution
Send over 2 Cannibals
Send one Cannibal back
Send over 2 Missionaries
Send one Cannibal and one Missionary back
Send over 2 cannibals
Send one cannibal back

29. Revised problem Five missionaries and five cannibals
Want to cross a river using one canoe.
Canoe can hold up to three people.
Can never be more cannibals than missionaries on either side of the river.
Aim: To get all safely across the river without any missionaries being eaten.
States?? Actions?? Goal test?? Path cost??

30. Revised Problem Solution
Send over 3 Cannibals
Send 1 Cannibal back
Send over 2 Cannibals
Send over 3 Missionaries
Send one Cannibal and one Missionary back
Send one Cannibal back
Send over 3 cannibals
Send one cannibal back
Send over 2 cannibals