8/7/2019 TTNT-03-Game

1/29

TR TU NHN T OTm ki m i khng Tr chi

8/7/2019 TTNT-03-Game

2/29

2 N i dung trnh byTr chiTr chi i khng v tm ki mThu t ton MINIMAX

-Hm l ng gi, Tm ki m c t nhnh

8/7/2019 TTNT-03-Game

3/29

Tr chiL m t trong nh ng c tnh c xem lthng minh c a con ng iF1 c a AI

3

y ta xem xt cc d ng tr chi tr tu , i

khng (board game)

8/7/2019 TTNT-03-Game

4/29

Tr chiC vua

1997, DeepBlue nh b i Gary Kasparov trongm t tr n u 6 vnB quy t:

4

Tm ki m vt c n v i su cao nh t c thTnh c 200.000.000 n c i m i giy so v i 2 c aKasparov

(99.99% n c i c xem l ngu ng c)Hm l ng gi c c k ph c t p

8/7/2019 TTNT-03-Game

5/29

Tr chi (tt)M t s khc: C vy (GO): v n cha c chng trnh hi uqu (do phn nhnh qu l n, b> 300)

5

8/7/2019 TTNT-03-Game

6/29

Tr chi i khng v tm ki mCc thnh ph n:

T p tr ng thi: t p c u hnh h p l c a tr chiTr ng thi ban u (initial state)Tr ng thi k t thc (terminal state), tr ng thi ch

6

Hm l i ch (utility function): nh gi tr ng thik t thc

Hai ng i chi: MAX vs. MIN

Khng tm ng i, tm n c i t t nh t.N c i c a MAX ph thu c vo n c i c aMIN v ng c l i.

8/7/2019 TTNT-03-Game

7/29

V d cy tm ki m tr chi - TicTacToe

XX

X

X

XX

MAX(x)

MIN(o)

Cc n c i7

XO X O

XO XO XO

XO XO O XX XO

XO XX

XO O

MAX(x)

K T THC

L i ch -1 0 +1

Cc tr ng thi

8/7/2019 TTNT-03-Game

8/29

Thu t ton MINIMAXNh ng ng i chi l t i u

MAX t i a ha hm l i chMIN t i thi u ha hm l i chChi n l c c a MAX h thu c vo chi n l c

8

c a MIN b c sau

Gi tr MINIMAX-VALUE: ti n ch tr ng thik t thc tng ng c a ng i, gi snh ng ng i chi lun t i u

8/7/2019 TTNT-03-Game

9/29

Gi tr MINIMAXMINIMAX-VALUE(n) =

Utility(n) n u n l tr ng thi k t thc max{MINIMAX-VALUE(s) | ssuccs(n)}

n u n l m t nt MAX

9

min{MINIMAX-VALUE(s) | ssuccs(n)}

n u n l m t nt MIN

8/7/2019 TTNT-03-Game

10/29

Gi tr MINIMAX (vd)A

B C D

MAX

MIN

10

3 12 8 2 4 6 14 5 2

tr ng thi k t thc,gi tr MINIMAX-

VALUE(n) = Utility(n)

8/7/2019 TTNT-03-Game

11/29

Gi tr MINIMAX (vd)A

B C D

MAX

MIN 3 2 2

11

3 12 8 2 4 6 14 5 2T i m i tr ng thi c th , MIN lun ch n ng it i thi u ha gi tr ti n ch tr ng thi k t thc

8/7/2019 TTNT-03-Game

12/29

Gi tr MINIMAX (vd)A

B C D

MAX

MIN 3 2 2

n l t mnh, MAX tmcch t i a ha gi tr

MINIMAX

3

12

3 12 8 2 4 6 14 5 2

V MAX ch n chi n l ci n B ng v i gi tr

MINIMAX t i a

8/7/2019 TTNT-03-Game

13/29

Thu t ton MINIMAX13

8/7/2019 TTNT-03-Game

14/29

nh gi Thu t gi i MINIMAX y ? C (n u cy tm ki m h u h n)

T i u?C (v i m t i th t i u) ph c t p th i gian?O(bm)

m

14

chi u su)

V i c vua, b 35, m 100 v i m t vn thngth ng hon ton khng th tm c l i gi it i u

8/7/2019 TTNT-03-Game

15/29

8/7/2019 TTNT-03-Game

16/29

T a nhnh - (vd)A

B[-;3]

[-; +] A

B[-;3]

[-; +]Mi n tr gi trMiniMax c a

MAX

16

3a)

3 12b)Mi n tr gi tr

MiniMax c aMIN

8/7/2019 TTNT-03-Game

17/29

T a nhnh - (vd)A

B[3;3]

[3; +] A

B C D[3;3]

[3;+]

[-;2]

17

3 1 2 8c)

3 12 8 2d)

8/7/2019 TTNT-03-Game

18/29

T a nhnh - (vd)A

B C D[3;3]

[3; 14]

[-;2] [-;14]

A

B C D[3;3]

[3;3]

[-;2] [2;2]

18

e)3 1 2 8 2 14

f)23 12 8 14 5 2

8/7/2019 TTNT-03-Game

19/29

T a nhnh - (vd)G i x, y l l i ch c a cc tr ng thi khng xt. Ta c:

MINIMAX-VALUE(g c) = max(min(3,12,8),min(2,x,y),min(14,5,2))

19

= max(3, min(2,x,y), 2)= max(3, z, 2) v i z

8/7/2019 TTNT-03-Game

20/29

8/7/2019 TTNT-03-Game

21/29

Thu t ton -21

8/7/2019 TTNT-03-Game

22/29

Thu t ton - (tt)22

8/7/2019 TTNT-03-Game

23/29

Ngh tr c gi i h n v hm l nggi

Cc tr chi th ng c su l n (>35 i v i

c vua)Trong th i gian th c, khng th i n tr ng thik t thc nh gi m t n c i -> ngh tr c

23

C n m thm l ng gicc tr ng thi khng k tthc thay cho hm nh gi l i ch c a tr ngthi k t thc.Hm l ng gi l m t heuristic.

8/7/2019 TTNT-03-Game

24/29

Ngh tr c gi i h n v hm l nggi (tt)24

8/7/2019 TTNT-03-Game

25/29

S b c ngh tr c25

8/7/2019 TTNT-03-Game

26/29

Hm l ng ginh gi kh nng thnh cng c a m t n c i (th ng,thua, ha?)nh gi tuy n tnh t ng cc c trng c c c a m t i th

Eval(s) = w1 f 1(s) + w2 f 2(s) + + wn f n(s)

26

rong : wi: r ng s g n c o qu n(v d : h u w=9, ng a w= 3)

f i: s qun cn l i

MiniMaxCutoff gi ng h t tm ki mMiniMaxValuetr :Thay Terminal? b ng Cutoff?Thay Utility()b ng Eval()

8/7/2019 TTNT-03-Game

27/29

Chng trnh game27

8/7/2019 TTNT-03-Game

28/29

i u c n n mCc thnh ph n tr chi, MIN, MAX

Thu t ton MINIMAX, thu t ton -nh gi c a cc thu t ton

28

8/7/2019 TTNT-03-Game

29/29

Th c m c29