SP14 CS188 Lecture 3 -- Informed Search

8/15/2019 SP14 CS188 Lecture 3 -- Informed Search

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CS 188: Artifcial Intelligence

Inormed Search

Instructors: Dan Klein and Pieter Abbeel

Universit o Caliornia! "er#ele$%hese slides &ere created b Dan Klein and Pieter Abbeel or CS188 Intro to AI at UC "er#ele' All CS188 m


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%oda

Inormed Search +euristics

,reed Search

A- Search

,ra(h Search


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.eca(: Search


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.eca(: Search

Search (roblem: States /confgurations o the &orld0 Actions and costs Successor unction /&orld dnamics0 Start state and goal test

Search tree: odes: re(resent (lans or reaching states Plans have costs /sum o action costs0

Search algorithm: Sstematicall builds a search tree Chooses an ordering o the ringe /une2(lored

nodes0

3(timal: fnds least4cost (lans


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52am(le: Panca#e Problem

Cost: umber o (anca#es 6i((ed


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7

9

7

7

9

State s(ace gra(h &ith costs as &eights

7

9

7

9


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,eneral %ree Search

Action: 6i( to(t&o

Cost:

Action: 6i( allour

Cost: 9

Path to reachgoal:

li( our! 6i(three

%otal cost: ;


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%he 3ne


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Uninormed Search


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Uniorm Cost Search

Strateg: e2(and lo&est (ath cost

%he good: UCS is com(lete ando(timal?

%he bad: 52(lores o(tions in ever @direction o inormation about goal location

Start

…

$Demo: contours UC$Demo: contours UC


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ideo o Demo Contours UCS 5

ideo o Demo Contours UCS Pa


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ideo o Demo Contours UCS PaSmall Eae


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Inormed Search


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Search +euristics

A heuristic is: A unction that estimates ho& close a state is

to a goal Designed or a (articular search (roblem

52am(les: Eanhattan distance! 5uclideandistance or (athing

10

5

11.2


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52am(le: +euristic unction

h(x)


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+euristic: the number o the largest (anca#e that is(lace

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0

2

3

3

3

4

4

3

4

4

4

h(x)


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,reed Search


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h(x)


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,reed Search

52(and the node that seems closestF

Ghat can go &rongH


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,reed Search

Strateg: e2(and a node that ou

thin# is closest to a goal state +euristic: estimate o distance to

nearest goal or each state

A common case:

"est4frst ta#es ou straight to the/&rong0 goal

Gorst4case: li#e a badl4guided DS

…

…

$Demo: contours greed$Demo: contours greed

id d /


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ideo o Demo Contours ,reed /


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A- S h


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A- Search

A- S h


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A- Search

UCS ,reed

A-

C bi i UCS d , d


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Combining UCS and ,reed

Uniorm4cost orders b (ath cost! or backward cg/n0

,reed orders b goal (ro2imit! or forward costh/n0

A- Search orders b the sum: /n0 /n0 J h/n0

S a d

b

G

h=5

h=6

h=2

1

8

1

1

2

h=6 h=0

c

h=7

3

e h=1

1a

b

c

d

G

g =1

h=5

g =2

h=6g =3

h=7

Gh h ld A- t i t H


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Ghen should A- terminateH

Should &e sto( &hen &e en=ueue

o: onl sto( &hen &e de=ueue a g

S

B

A

G

2

3

2

2

h = 1

h = 2

h = 0h = 3


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Idea: Admissibilit


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Idea: Admissibilit

Inadmissible /(essimistic0 heuristicsbrea# o(timalit b tra((ing good

(lans on the ringe

Admissible /o(timistic0do&n bad (lans but n

true cost

Admissible +euristics


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Admissible +euristics

A heuristic h is admissible /o(timistic0 i:

&here is the true cost to a nearest

52am(les:

Coming u( &ith admissible heuristics is mo&hatLs involved in using A- in (ractice'

915

3(timalit o A- %ree Search


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Assume:

A is an o(timal goal node

" is a subo(timal goal node

h is admissible

Claim:

A &ill e2it the ringe beore "

F


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3(timalit o A- %ree Search: "lo


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Proo:

Imagine " is on the ringe

Some ancestor n o A is onthe ringe! too /mabe A?0

Claim: n &ill be e2(andedbeore "

1' /n0 is less or e=ual to

/A0' /A0 is less than /"0 "

h

F



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Proo:

Imagine " is on the ringe

Some ancestor n o A is onthe ringe! too /mabe A?0

Claim: n &ill be e2(andedbeore "

1' /n0 is less or e=ual to

/A0' /A0 is less than /"0

7' n e2(ands beore "

All ancestors o A e2(andbeore "

A e2(ands beore "

F


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Pro(erties o A-

Pro(erties o A-


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Pro(erties o A

Fb

Fb

Uniorm4

Cost

A-

UCS vs A- Contours


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UCS vs A Contours

Uniorm4cost e2(ands e=uall

in all @directions

A- e2(ands mainl to&ard thegoal! but does hedge its betsto ensure o(timalit

Start

Start

$Demo: contours UCS )

em(t /B7D10*

ideo o Demo Contours /5m(t0


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ideo o Demo Contours /5m(t0

ideo o Demo Contours /5m(t


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/ (,reed



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ideo o Demo Contours /PacmanE 0 A-


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/Eae0 O A-


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A- A((lications


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A A((lications

A- A((lications


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A A((lications

ideo games

Pathing ) routing (roblems .esource (lanning (roblems

.obot motion (lanning

Banguage analsis

Eachine translation S(eech recognition

F

$Demo: UCS ) A- (acman

/B7D!B7D;0*


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ideo o Demo 5m(t Gater Shallo&)Dee(Algorithm


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Algorithm

Creating +euristics


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g

Creating Admissible +euristics


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g

Eost o the &or# in solving hard search (roblems is in coming u( &ith admissible heuristics

3ten! admissible heuristics are solutions to relaxe problems &here ne& actions are available

Inadmissible heuristics are oten useul too

15366

52am(le: 8 Pule


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(

Ghat are the statesH +o& man statesH Ghat are the actionsH +o& man successors rom the start

stateH

Ghat should the costs beH

Start State ,Actions

8 Pule I


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+euristic: umber o tilesmis(laced

Gh is it admissibleH h/start0

%his is a relaxed!problem heuristic

8

Average nodese2(anded &heo(timal (ath h

F9ste(s

F8ste(s

UCS 11 !7MM

Start State

St

8 Pule II


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Ghat i &e had an easier 84(ule&here an tile could slide andirection at an time! ignoringother tilesH

%otal "anhattan distance

Gh is it admissibleH

h/start0 7 J 1 J J F 18

Average nodee2(anded &ho(timal (ath

F9ste(s

F8ste(s

%IB5S 17 7Q

Start State

8 Pule III


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+o& about using the act#al cost as a heuristicH Gould it be admissibleH

Gould &e save on nodes e2(andedH

GhatLs &rong &ith itH

Gith A-: a trade4oR bet&een =ualit o estimate a(er node As heuristics get closer to the true cost! ou &ill e2(and

nodes but usuall do more &or# (er node to com(ute thheuristic itsel


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Semi4Battice o +euristics


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,ra(h Search


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%ree Search: 52tra Gor#?


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ailure to detect re(eated states can cause e2(onmore &or#'

Search %reeState ,ra(h

,ra(h Search


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In "S! or e2am(le! &e shouldnLt bother e2(anding thnodes /&hH0

S

a

b

d p

a

c

e

p

h

f

r

$

$ c ,

a

$e

p

h

f

r

$

$ c %

a

,ra(h Search


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Idea: never e2(and a state t&ice

+o& to im(lement: %ree search J set o e2(anded states /@closed set0

52(and the search tree node4b4node! butF

"eore e2(anding a node! chec# to ma#e sure its sthas never been e2(anded beore

I not ne&! s#i( it! i ne& add to closed set

Im(ortant: store the closed set as a set! not a

Can gra(h search &rec# com(letenessH

Gh)&h notH

+o& about o(timalitH

A- ,ra(h Search ,one GrongH


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S

A

"

C

G

1

1

1

7

h=2

h=1

h=4

h=1

h=0

S /MJ0

A /1J90 " /1

C /J10

, /NJM0

C /7

, /

State s(ace gra(h Search tree

Consistenc o +euristics


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Eain idea: estimated heuristi

actual costs

Admissibilit: heuristic cost T ac

goal

h/A0 T actual cost rom A to

Consistenc: heuristic @arc cos

or each arc

h/A0 O h/C0 T cost/A to C0

Conse=uences o consistenc

%he value along a (ath never d

h/A0 T cost/A to C0 J h/C0

7

A

C

G

h=4 h=1

1

h=2

3(timalit o A- ,ra(h Search


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3(timalit o A- ,ra(h Search


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S#etch: consider &hat A- does

&ith a consistent heuristic: act 1: In tree search! A- e2(ands

nodes in increasing total value /4contours0

act : or ever state s! nodesthat reach s o(timall aree2(anded beore nodes that reachs subo(timall

.esult: A- gra(h search is o(timal

F

3(timalit


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%ree search: A- is o(timal i heuristic is admissible UCS is a s(ecial case /h M0

,ra(h search: A- o(timal i heuristic is consistent UCS o(timal /h M is consistent0

Consistenc im(lies admissibilit

In general! most natural admissibleheuristics tend to be consistent!es(eciall i rom rela2ed (roblems

A-: Summar


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A-: Summar


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A- uses both bac#&ard costs and /estimatesor&ard costs

A- is o(timal &ith admissible ) consistent he

+euristic design is #e: oten use rela2ed (r

%ree Search Pseudo4Code


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,ra(h Search Pseudo4Code


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SP14 CS188 Lecture 3 -- Informed Search

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Transcript of SP14 CS188 Lecture 3 -- Informed Search