Artificial Intelligence
CS 165A
Thursday, October 4, 2007
 Intelligent agents (Ch. 2)
 Blind search (Ch. 3)
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Notes
• New room!
2
Review
• What is an agent?
– An entity capable of combining cognition, perception and action in
behaving autonomously, purposively and flexibly in some
environment
• What does an agent do?
– An agent perceives its environment, reasons about its goals, and
acts upon the environment
• What does PEAS stand for (description of an agent)?
– Performance measure, Environment, Actuators, Sensors
• What are we about to do right now?
3
Thursday Quiz #1
Write your name, your perm #, and the date at the top of the page
1. Humans often solve NP-complete problems in times much
shorter than the complexity limits. Does McCarthy
consider this evidence that computers are intrinsically
incapable of doing what people do?
2. Why or why not?
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Generic Agent Program
• Implementing f : P*  A
…or…
f (P*) = A
– Lookup table?
– Learning?
Knowledge, past percepts, past actions
e.g.,
Table-Driven-Agent
Add percept to percepts
LUT [percepts, table]
NOP
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Basic types of agent programs
• Simple reflex agent
• Model-based reflex agent
• Goal-based agent
• Utility-based agent
• Learning agent
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Simple Reflex Agent
• Input/output associations
• Condition-action rule: “If-then” rule (production rule)
– If condition then action (if in a certain state, do this)
– If antecedent then consequent
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Simple Reflex Agent
• Simple state-based agent – Classify the current percept
into a known state, then apply the rule for that state
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Model-Based Reflex Agent
• Internal state – keeps track of the world, models the world
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Model-Based Reflex Agent
• State-based agent – Given the current state, classify the
current percept into a known state, then apply the rule
for that state
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Goal-Based Agent
• Goal: immediate, or long sequence of actions?
– Search and planning – finding action sequences that achieve the
agent’s goals
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Utility-Based Agent
• “There are many ways to skin a cat”
• Utility function: Specifies degree of usefulness (happiness)
– Maps a state onto a real number
1
U
cost
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Learning Agent
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Environments
• Properties of environments
–
–
–
–
–
–
–
Fully vs. partially observable
Deterministic vs. stochastic
Episodic vs. sequential
Friendly vs. hostile
Static vs. dynamic
Discrete vs. continuous
Single agent vs. multiagent
• The environment types largely determine the agent design
• The real world is inaccessible, stochastic, nonepisodic,
hostile, dynamic, and continuous
– Bummer…
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Problem Solving and Search
Chapter 3
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Problem Solving Agents
• Task: Find a sequence of actions that leads to desirable
(goal) states
– Must define problem and solution
• Finding a solution is typically a search process in the
problem space
– Solution = A path through the state space from the initial state to a
goal state
– Optimal search find the least-cost solution
• Search algorithm
– Input: Problem statement (incl. goal)
– Output: Sequence of actions that leads to a solution
• Formulate, search, execute (action)
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Search Strategies
• Uninformed (blind) search (Chap. 3)
– Can only distinguish goal state from non-goal state
• Informed (heuristic) search (Chap. 4)
– Can evaluate states
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Problem Formulation and Search
• Problem formulation
– State-space description < {S}, S0, {SG}, {O}, {g} >
 S: Possible states
 S0: Initial state of the agent
 SG: Goal state(s)
– Or equivalently, a goal test G(S)
 O: Operators O: {S} => {S}
– Describes the possible actions of the agent
 g: Path cost function, assigns a cost to a path/action
• At any given time, which possible action Oi is best?
– Depends on the goal, the path cost function, the future sequence of actions….
• Agent’s strategy: Formulate, Search, and Execute
– This is offline (or batch) problem solving
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Typical assumptions for simple PS agent
• Environment is observable
• Environment is static
• Environment is discrete
• Environment is deterministic
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State-Space Diagrams
• State-space description can be represented by a statespace diagram, which shows
– States (incl. initial and goal)
– Operators/actions (state transitions)
– Path costs
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Example: Romania
You’re in Arad, Romania, and you need to get to Bucharest as
quickly as possible to catch your flight.
• Formulate problem
– States: Various cities
– Operators: Drive between cities
• Formulate goal
– Be in Bucharest before flight leaves
• Find solution
– Actual sequence of cities from Arad to Bucharest
– Minimize driving distance/time
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Romania (cont.)
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Romania (cont.)
Problem description <{S}, S0, {SG}, {O}, {g}>
• {S} – cities (ci)
• S0 – Arad
• SG – Bucharest
– G(S) – Is the current state (S) Bucharest?
• {O}: { ci  cj, for some i and j }
• gij
– Driving distance between ci and cj?
– Time to drive from ci to cj?
– 1?
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Possible paths
Arad
Zerind
Sibiu
Oradea
Fagaras
Sibiu
Bucharest
Timisoara
R. Vilcea
Pitesti
Bucharest
Lugoj
Mehadia
Dobreta
Which is best?
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Branching Factor
• If there are N possible choices at each state, then the
branching factor is N
• If it takes M steps (state transitions) to get to the goal state,
then it may be the case that O(NM) states have to be
checked
– N = 3, M = 5  NM = 243
– N = 5, M = 10  NM = 9,765,625
– N = 8, M = 15  NM = 35,184,372,088,832
• Ouch…. Combinatorial explosion!
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Abstraction
• The real world is highly complex!
– The state space must be abstracted for problem-solving
 Simplify and aggregate
– Can’t represent all the details
• Choosing a good abstraction
– Remove as much detail as possible while retaining validity
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Example Problem: 8-Puzzle
States: Various configurations of the puzzle
Operators: Movements of the blank
Goal test: State matches goal state
Path cost: Each move costs 1
How many states
are there?
9! = 362,880
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One way to represent the state
Action
======
Start State:
5*9^0 + 4*9^1 + 0*9^2
+ 6*9^3 + 1*9^4 + 8*9^5
+ 7*9^6 + 3*9^7 + 2*9^8
= 104645804
Goal State:
1*9^0 + 2*9^1 + 3*9^2
+ 8*9^3 + 0*9^4 + 4*9^5
+ 7*9^6 + 6*9^7 + 5*9^8
= 247893796
>
^
^
>
V
V
<
^
<
V
>
^
^
<
V
>
>
^
<
V
State
=====
091150500
086898972
110781012
110826876
110826300
110590428
024615084
215933844
249368700
249403692
248872980
219112284
247770732
247823148
247823172
247822444
247775788
247670812
247906684
247906900
247893796 28
8-Puzzle is hard (by definition)!
• Optimal solution of the N-puzzle family of problems is
NP-complete
– Exponential increase in computation with N
– Uninformed search will do very poorly
• Ditto for the Traveling Salesman Problem (TSP)
– Start and end in Bucharest, visit every city at least once
– Find the shortest tour
• Ditto for lots of interesting problems!
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Example: MU-Puzzle
•
•
States: Strings comprising the letters M, I, and U
Initial state: MI
•
•
Goal state: MU
Operators: (where x stands for any string, including the null string)
1.
2.
3.
4.
x I  x IU
MxMxx
xI I Ix  xUx
xUUx  xx
“Append U”
“Replicate x”
“Replace with U”
“Drop UU”
Each rule describes the whole string, not a subset
•
Path cost: one per step
•
Try it
– Can you draw the state-space diagram?
– Are you guaranteed a solution?
MI
MII
MIIII
MUI
MUIU
MUIUUIU
MUIUUIUUIUUIU
MUIIIIU
MUUIU
MIU
…
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•
Clarification of the MU-puzzle rules:
1. If the string ends with I you may add U; for example, MI becomes
MIU
2. If the string is Mx then you may create Mxx; for example, MI
becomes MII; MIU becomes MIUIU
3. If the string contains III you may replace those three characters
with U
4. If the string contains UU you may eliminate both characters
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Example: The Vacuum World
• Simplified world: 2 grids
States: Location of vacuum, dirt in grids
Operators: Move left, move right, suck dirt
Goal test: Grids free of dirt
Path cost: Each action costs 1
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The Vacuum World (cont.)
• How to reach the goal?
– If starting at top left state: S, R, S
– If starting at middle far right state: L, S
• What if agent doesn’t know its initial state?
– You probably need to redraw the state diagram!
– Represent initial uncertainty as one “meta-state”
 For example…
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