2 TD ( ) (1) Minimax Minimax () () PV(Principal Variaion) 2
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- きょういち さわまつ
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1 TD TD 1.2 TD TD 3 4 1
2 2 TD ( ) (1) Minimax Minimax () () PV(Principal Variaion) 2
3 45 A 45 B 30 C 20 D E F G H I J K L M N O P Q R S T U V W X 1Minimax 1 K E F A,B,E,N PV (Negamax Form) 2 in Minimax(node_ n, in d){ in i, score = - ; if(d == 0 n == erminal) reurn Evaluae(n); for(i = 0; i < n.num_of_children; i++){ g = Minimax(n.child_node[i], d-1) score =max(score, g); } } 2Minimax (Negamax Form) 3
4 2.1.4 Alpha-Bea Alpha-Bea Minimax 3Alpha-Bea 3 G A 45 C C D Minimax 2 4 Alpha-Bea (Negamax Form) 4
5 in AlphaBea(node_ n, in d, in _, in _){ in score = - ; if(d == 0 n == erminal) reurn Evaluae(n); for(i = 0; i < n.num_of_children; i++){ score = max(score, -AlphaBea(n.child_node[i], d-1, -_, -_)); _ = max(_, score); } } if( ) reurn _; reurn score; 4Alpha-Bea 2.2 TD TD(Temporal Difference) TD TD TD(Temporal Difference) ( 1 ) TD 1 () TD TD TD TD(0) S s S V(s ) s +1 V(s +1) V(s ) V ( s ) V ( s ) + [ V ( s+ 1) V ( s )] (2) 0<1 5
![child_node[i], d-1, -_, -_)); _ = max(_, score); } } if( ) reurn _; reurn score; 4Alpha-Bea 2.](/docs-images/42/22849204/images/page_5.jpg "2 TD TD(Temporal Difference) TD 2.2.1 TD TD(Temporal Difference) ( 1 ) TD 1 () TD 1 1 1 1 TD TD TD(0) S s S")
6 TD(0) TD() V k ( sk ) V ( sk ) + [ V ( s+ 1 ) V ( s )] (3) 1k k (3) 01 =0 TD(0) TD 1 1 V(s ) ( ) P 2 MSE MSE( ) = s S P( s)[ V ( s) V ( s)] V (s) s 2 T = ( (1), (2),..., ( n)) V (s) ss 2 s [ V + 1 ( s ) V ( s )] 2 (4) TD(0) = [ V 1( s ) V ( s )] + = + [ V ( s ) V ( s )] V ( s ) + 1 (5) TD() k 1 [ V ( s 1) V ( s )] V ( sk ) (6) k = 1 6
7 2 5 0 e = s_ s V(s) - V(s) e e + V ( s) + e s s' s 5TD() n T V ( s) = = ( i) ( i) s i= 1 s V ( s) = (8) s 1 (7) TDLEAF() TD Principal Variaion TD() TDLEAF() 7
8 2.2.4 TD KnighCap KnighCap TD Alpha-Bea 5 [3] 5 1 8
9 (10 50 ) TDLEAF() 0.9 9
10 [-99999,99999] (9) 6 P = 1 1+ e (9) ( E) E /1000 E P( 1260) = / e 1260 = 0.78 (10) dp de = P(1 P) P E P = E i i 1 = i P(1 P) 1000 (11) (12) (6)(0,1] 20 1 ()
11 3.3 TD while(1){ } _ while(1){ if() else if(){ principal variaion principal variaion } } 7 11
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18 ( )
19 TDLEAF() KnighCap TD KnighCap KnighCap
20 5 5.1 TD TD
21 1 21
22 [1]Jonahan BaxerLearning To Play Chess Using Temporal Differences. [2]Richard S. Suon, Andrew G.Baro, (2000 ). [3]TD (1999 ). [4],,TD (1999 GPW 99 ). [5]Akihiro KishimooTransposiion Table Driven Scheduling for Two-Player Games, M.Sc. Thesis, Universiy of Albera (Final version), January [6],,, [7],(1998 ) 22
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