ttnt-03-game
TRANSCRIPT
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TR TU NHN T OTm ki m i khng Tr chi
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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
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Tr chiL m t trong nh ng c tnh c xem lthng minh c a con ng iF1 c a AI
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y ta xem xt cc d ng tr chi tr tu , i
khng (board game)
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Tr chiC vua
1997, DeepBlue nh b i Gary Kasparov trongm t tr n u 6 vnB quy t:
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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
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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)
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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
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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.
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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
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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
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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
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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
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min{MINIMAX-VALUE(s) | ssuccs(n)}
n u n l m t nt MIN
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Gi tr MINIMAX (vd)A
B C D
MAX
MIN
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3 12 8 2 4 6 14 5 2
tr ng thi k t thc,gi tr MINIMAX-
VALUE(n) = Utility(n)
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Gi tr MINIMAX (vd)A
B C D
MAX
MIN 3 2 2
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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
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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
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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
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Thu t ton MINIMAX13
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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
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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
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T a nhnh - (vd)A
B[-;3]
[-; +] A
B[-;3]
[-; +]Mi n tr gi trMiniMax c a
MAX
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3a)
3 12b)Mi n tr gi tr
MiniMax c aMIN
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T a nhnh - (vd)A
B[3;3]
[3; +] A
B C D[3;3]
[3;+]
[-;2]
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3 1 2 8c)
3 12 8 2d)
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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]
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e)3 1 2 8 2 14
f)23 12 8 14 5 2
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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))
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= max(3, min(2,x,y), 2)= max(3, z, 2) v i z
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Thu t ton -21
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Thu t ton - (tt)22
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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
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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.
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Ngh tr c gi i h n v hm l nggi (tt)24
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S b c ngh tr c25
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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)
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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()
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Chng trnh game27
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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
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Th c m c29