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Artificial Intelligence

CS 165A

Thursday, October 4, 2007

Intelligent agents (Ch. 2) Blind search (Ch. 3)

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Notes

• New room!

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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?

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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

Add percept to percepts

LUT [percepts, table]

NOP

Table-Driven-Agent

e.g.,

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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 cost

1U

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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 state-space 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

Sibiu

Oradea

Zerind

Bucharest

PitestiBucharest

Fagaras R. Vilcea

Sibiu

Dobreta

Mehadia

Lugoj

Timisoara

Arad

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 puzzleOperators: Movements of the blankGoal test: State matches goal statePath cost: Each move costs 1

How many states are there?

9! = 362,880

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One way to represent the stateAction State====== ===== 091150500 > 086898972 ^ 110781012 ^ 110826876 > 110826300 V 110590428 V 024615084 < 215933844 ^ 249368700 < 249403692 V 248872980 > 219112284 ^ 247770732 ^ 247823148 < 247823172 V 247822444 > 247775788 > 247670812 ^ 247906684 < 247906900 V 247893796

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

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

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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. x I x IU “Append U”2. M x M x x “Replicate x”3. xI I Ix xUx “Replace with U”4. xUUx xx “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?

M I

M I I

M I I I I

M U I

M U I U

M U I U U I U

M U I U U I U U I U U I U

M U I I I I U

M U U I U

M I U

…

M I

M I I

M I I I I

M U I

M U I U

M U I U U I U

M U I U U I U U I U U I U

M U I I I I U

M U U I U

M I U

…

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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…