Artificial Intelligence

CS 165A Thursday, October 4, 2007   Intelligent agents (Ch. 2) Blind search (Ch. 3)

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?

4

Generic Agent Program • Implementing

f : P*



A

– Lookup table?

– Learning?

…or…

f (P*) = A

Knowledge, past percepts, past actions e.g.,

Table-Driven-Agent

Add

percept

to percepts LUT [percepts, table] NOP 5

Basic types of agent programs

• Simple reflex agent • Model-based reflex agent • Goal-based agent • Utility-based agent • Learning agent 6

Simple Reflex Agent

• Input/output associations • Condition-action rule: “If-then” rule (

production rule

) – If

condition

– If

antecedent

then

action

then (if in a certain state, do this)

consequent

7

Simple Reflex Agent

• Simple state-based agent – Classify the current percept into a known state, then apply the rule for that state 8

Model-Based Reflex Agent

• Internal state – keeps track of the world, models the world 9

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 10

Goal-Based Agent

• Goal: immediate, or long sequence of actions?

– Search and planning – finding action sequences that achieve the agent’s goals 11

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

U



1

Learning Agent

13

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… 14

Problem Solving and Search

Chapter 3 15

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) 16

Search Strategies

• Uninformed (blind) search (Chap. 3) – Can only distinguish goal state from non-goal state • Informed (heuristic) search (Chap. 4) – Can evaluate states 17

Problem Formulation and Search

• Problem formulation – State-space description

< {S}, S 0 , {S G }, {O}, {g} >



S

: Possible states  

S 0

: Initial state of the agent

S G

: 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

O i

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 18

Typical assumptions for simple PS agent

• Environment is observable • Environment is static • Environment is discrete • Environment is deterministic 19

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 20

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 21

Romania (cont.)

22

Romania (cont.)

• • • Problem description

<{S}, S 0 , {S G }, {O}, {g}> {S} –

cities (c i )

S 0 –

Arad

S G –

Bucharest – G(S) – Is the current state (S) Bucharest?

• • {O}: { c i  c j , for some

i

and

j

}

g ij

– Driving distance between c – Time to drive from c i – 1?

to c j ?

i and c j ?

23

Possible paths

Zerind Oradea Sibiu Arad Sibiu Fagaras Bucharest R. Vilcea Pitesti Bucharest

Which is best?

Timisoara Lugoj Mehadia Dobreta 24

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(

N M )

states have to be checked – – –

N

= 3,

M N N

= 5, = 8,

M M

= 5  = 10 

N M N M =

243

=

9,765,625 = 15 

N M =

35,184,372,088,832 • Ouch…. Combinatorial explosion!

25

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

26

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 27

One way to represent the state

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 Action 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

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!

29

Example: MU-Puzzle

• • • • • • States: Strings comprising the letters M, I, and U Initial state: MI Goal state: MU Operators: (where

x

1.

2.

3.

4.

x

I 

x

IU M

x x

I I I 

x

M 

x x x

U

x x

UU

x



xx

Try it stands for any string,

including the null string

) “Append U”

“

Replicate

x

” “Replace with U” “Drop UU” Each rule describes the whole string, not a subset Path cost: one per step – 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 … 30

• 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 31

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 32

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… 33