Research on decision making in multi-player games with imperfect information
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1 Research on decision making in multi-player games with imperfect information
2 UCT UCT 46 % %
3 UCT Minimax UCT UCT UCT Bonanza SVD-ASO SVM i
4 UCT ii
5 2.1 *-Minimax tree search. [Hauk, 2004] A sample max n Tree. [Sturtevant, 2003] UCT [Schäfer, 2008] UCT ( / ) [Kitagawa et al., 2007] [Miki et al., 2008] [Miki et al., 2008] Text categorization performance results. [Ando et al., 2005] Comparison with co-training. [Ando et al., 2005] Support Vector Machine (22 ) (22 ) ( 396 ) ( 396 ) (22 F 0.4 ) (22 F 0.4 ) (396 F 0.1 ) (396 F 0.1 ) iii
6 2.1 ( ) (10000 ) UCB C (10000 ) SVM SVM UCT ( ) SVM UCT ( ) [Kitagawa et al., 2007] (22 F ) (400 ) (22 ) (400 ) iv
7 1 1.1 ( ) UCT (UCB applied to Trees) [11] Minimax UCT UCT 1
8
9
10 UCT 3 4 4
11 2 UCT 2.1 Minimax Minimax Minimax [3][7] Minimax UCT (UCB applied to Trees) [11] UCT UCT [15][13] UCT UCT UCT 5
12 UCT Minimax UCT UCT UCT Minimax Minimax *-Minimax Max n *-Minimax Minimax Ballard *-Minimax [3][7] Minimax Min Max Chance Ballard Chance Alpha-Beta [8] 95% Max n Minimax Luckhardt Max n [12][14] Max n Max n Luckhardt UCT UCT (UCB applied to Trees) UCB Kocsis [2][11] UCT UCT UCT (2.1) UCB (Upper Confidence Bounds) 6
13 UCT 2.1: *-Minimax tree search. [Hauk, 2004] 2.2: A sample max n Tree. [Sturtevant, 2003] 7
14 UCT X i + C ln T T i (2.1) X i i T i i T C 1 2 [17] ( ) UCT UCT Sturtevant 3 UCT [15] 2.2 (b) 2 UCT (b) UCB (b) UCT Chinese Checkers ( ) UCT Max n 8
15 UCT 2.3: UCT [Schäfer, 2008] 2.4: UCT ( / ) 9
16 UCT UCT Schäfer Skat UCT [13] Skat Skat UCT Schäfer UCT Skat DDSS (Double Dummy Skat Solver) 2.3 Minimax UCT UCT UCT Minimax UCT UCT ( )
17 UCT 13 UCT Algorithm 1 UCT 14 UCB 13 ( ) UCB 4 11
18 UCT Algorithm 1 UCT while do i 0 node[i] while node[i] > 0 do if node[i] then break end if if then end if if then else node[i + 1] if node[i] 14 then node[i + 1] UCB else if node[i] 13 then node[i + 1] UCB end if end if i i + 1 end while while i 0 do node[i] i i 1 end while end while move 12
19 UCT 2.4 UCT CPU Core2 Duo 3GHz 2GB C UCT UCB C UCT C C 10 (2.2) f(x) = C 2 k e kx (2.2) 13
20 UCT C 2 k C UCT UCB C (2.1) C UCT C = UCT (2.1) C Random SVM SVM-rank[10][9] SVM UCT 46.1% SVM SVM [21][18] , 2.8 ( ) 14
21 UCT 2.1: ( ) [%] : (10000 ) [%] : UCB C (10000 ) C [%]
22 UCT 100 Accuracy rates [%] UCT best UCT best 3rd UCT best 5th Iterations Random SVM 2.5: Accuracy rates [%] Iterations UCT Random SVM 2.6: 13 16
23 UCT 100 Accuracy rates [%] Iterations UCT Random SVM 2.7: 100 Accuracy rates [%] Iterations UCT Random SVM 2.8: 17
24 UCT 2.4: SVM 1 18
25 UCT 2.5: SVM 2 1 boolean
26 UCT SVM UCT 1 5 (2.1) C ,2.7 UCT UCT SVM UCT 2.6: UCT ( ) Greedy A UCT A Greedy B UCT B [%] : SVM UCT ( ) SVM A UCT A SVM B UCT B [%]
27 Tesauro [16] 21
28 A B ( ) Bonanza Bonanza Bonanza [19] 2006 Bonanza Bonanza (3.1) l(s, θ) = M 1 m=1 T [ξ(s m, θ) ξ(s m=0, θ)] (3.1) θ : s m : s m M : s m = 0 : ξ(s m, θ) : Minimax T (x) 1 0 (3.2) k T (x) = e kx (3.2)
29 : [Kitagawa et al., 2007] [21] 1532 boolean ( 3.1) % SVM [18] SVM 53% 23
30 : [Miki et al., 2008] 3.3: [Miki et al., 2008] 24
31 : [Kitagawa et al., 2007]
![3.2. 3. 3.4: Text categorization performance results. [Ando et al., 2005] 3.2.4 SVD-ASO SVD-ASO (Singular Value](/docs-images/104/162175094/images/32-0.jpg "Decomposition-based Alternating Structure Optimization) Ando [1] SVD-ASO 1. 2. (SVD) 3. 1. ( ) 2. 2 SVD Ando 26")
32 : Text categorization performance results. [Ando et al., 2005] SVD-ASO SVD-ASO (Singular Value Decomposition-based Alternating Structure Optimization) Ando [1] SVD-ASO (SVD) ( ) 2. 2 SVD Ando 26
33 : Comparison with co-training. [Ando et al., 2005] k k co-training[4] 27
![3.2. 3. 3.6: Support Vector Machine 3.2.5 SVM SVM SVM[5] 1992 Vapnik 2 1 SVM ( ) ( ) w g(x) = w x + b 3.](/docs-images/104/162175094/images/34-0.jpg "6 y i x i 1-1 y i (w x + b) 1 2/ w n i=1 α iy i = 0 i α i 0 (3.")
34 : Support Vector Machine SVM SVM SVM[5] 1992 Vapnik 2 1 SVM ( ) ( ) w g(x) = w x + b 3.6 y i x i 1-1 y i (w x + b) 1 2/ w n i=1 α iy i = 0 i α i 0 (3.3) W (α) = n α i 1 2 i=1 n i=1 j=1 n α i α j y i y j x i x j (3.3) 28
35 ( ) ( )
36 SVD-ASO[1] (Principal Component Analysis) M ( ) P f ext f org, P Pf org P CA(M) = PM (3.4) f ext {f org, Pf org } (3.5) SVD-ASO P (Singular Value Decomposition) SV D(M) = UΣP T (3.6) f ext {f org, Pf org } (3.7) f ext f org c(f org ) f ext {f org, c(f org )} (3.8) f all f all {f org, Pf org, c(f org )} (3.9) 30
37 M c(f org ) = Mf org (3.10) w all f org I w allt f all = w allt Pf org = w allt P f org (3.11) Mf org = u T f org (3.12) 0 u (3.13) ( ) M = L(X, w) + C w 2 2 L : X : w : C : (3.13) SVM ( ) ( ) 31
38 : ( ) 4 ( ) 4 ( ) 4 ( ) 4 ( ) 4 *?? ( ) 4 *?? 1 1 ( ) 3 32
39 (10 ) 9. (5 )
40 ( ) (4 ) ( ) (5 4 ) ( ) ( ) ( ) ( ) ( ) 3.3:
41 ( ) ( ) InTrigger 2 kyushu hiro mirai 3 CPU Xeon E GHz 4Core Dual 16GB 200 CPU Opteron GHz 2Core Dual 32GB C++ SVM LIBLINEAR 3 L2 L2 SVM( ) SVDLIBC cjlin/liblinear/ 4 dr/svdlibc/ 35
42 % 46.9% fold cross validation 22 F fold cross validation F % 36
43 Accuracy [%] Training positions w/o auxiliary model prediction model and prediction 3.7: (22 ) 4 Missmatch Training positions w/o auxiliary model prediction model and prediction 3.8: (22 ) 37
44 Accuracy [%] Training positions w/o auxiliary model prediction model and prediction 3.9: ( 396 ) 4 Missmatch Training positions w/o auxiliary model prediction model and prediction 3.10: ( 396 ) 38
45 Accuracy [%] Training positions w/o auxiliary model prediction model and prediction 3.11: (22 F 0.4 ) 4 Missmatch Training positions w/o auxiliary model prediction model and prediction 3.12: (22 F 0.4 ) 39
46 Accuracy [%] Training positions w/o auxiliary model prediction model and prediction 3.13: (396 F 0.1 ) 4 Missmatch Training positions w/o auxiliary model prediction model and prediction 3.14: (396 F 0.1 ) 40
47 (22 F ) (22 ) : (22 F ) (400 ) prediction w/o A w/o B w/o C [%] : (22 ) (400 ) model w/o A w/o B w/o C [%]
48 4 4.1 UCT UCT UCT UCB1 UCB C C 1000 UCT ( ) 46 % 13 ( ) SVM UCT UCB C UCT 50% UCT 42
49 UCB C C 1000 (2.1) 1 2 [0,1] C UCT (2.1) % 50.6% [21][18] SVD-ASO 43
50 ( ) %
51 UCT 45
52 UCT [17] SVM UCT RAVE (Rapid Action Value Estimation) [6] [20] 46
53 2 w org = (w 0 w 1 ) T 1 w a a = (a 0 a 1 ) T w org = w w2 1 (1) w all = w w2 1 + w2 a (2) ( ) w allt f all = w allt f org ( ) = w 0 w 1 w a af org a 0 a 1 f org (3) = u T f org (4) u = ( w 0 + w a a 0 w 1 + w a a 1 ) (5) (5) u (w a a 0, w a a 1 ) ( ) w all 3 z = w a 47
54 [1] R.K. Ando and T. Zhang. A framework for learning predictive structures from multiple tasks and unlabeled data. The Journal of Machine Learning Research, Vol. 6, pp , [2] P. Auer, N. Cesa-Bianchi, and P. Fischer. Finite-time analysis of the multiarmed bandit problem. Machine Learning, Vol. 47, No. 2-3, pp , [3] BW Ballard. *-Minimax search procedure for trees containing chance nodes. Artificial Intelligence, [4] A. Blum and T. Mitchell. Combining labeled and unlabeled data with co-training. p. 100, [5] C. Cortes and V. Vapnik. Support-vector networks. Machine Learning, Vol. 20, No. 3, pp , [6] S. Gelly and D. Silver. Combining online and offline knowledge in UCT. Proceedings of the 24th international conference on Machine learning, pp , [7] T. Hauk. Search in trees with chance nodes. Master s thesis, University of Alberta, [8] T. Hauk, M. Buro, and J. Schäfer. Minimax performance in backgammon. Vol. 3846, pp , [9] T. Joachims. SVM-LIGHT: an implementation of Support Vector Machines (SVMs) in C. [10] T. Joachims. Optimizing search engines using clickthrough data. Proceedings of the ACM Conference on Knowledge Discovery and Data Mining (KDD), ACM, [11] L. Kocsis and C. Szepesvari. Bandit based monte-carlo planning. European Conference on Machine Learning, pp , [12] C. Luckhardt and K. Irani. An algorithmic solution of n-person games. AAAI, Vol. 1, pp , [13] J. Schäfer, M. Buro, and K. Hartmann. The UCT Algorithm Applied to Games with Imperfect Information. Diploma thesis. Otto-von-Guericke-Universität Magdeburg,
55 [14] N. Sturtevant. Last-Branch and Speculative Pruning Algorithms for Maxˆ n. IJCAI, Vol ,, [15] N.R. Sturtevant. An Analysis of UCT in Multi-player Games. Proceedings of the 6th international conference on Computers and Games, pp , [16] G. Tesauro. Connectionist learning of expert preferences by comparison training [17] Y. Wang and S. Gelly. Modifications of UCT and sequence-like simulations for Monte-Carlo Go. IEEE Symposium on Computational Intelligence and Games, CIG 2007, pp , [18],,.. Proceedings of 13th Game Programming Workshop, pp , [19].. Proceedings of 11th Game Programming Workshop, pp , [20]. UCT. Master s thesis,, [21],,.. Proceedings of 12th Game Programming Workshop,
56 [1],,. SVM. 13, pp , [2],,. UCT. 14, pp ,
57
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Title 中國宗教文獻研究國際シンポジウム報告書 ( 大規模佛教文獻群に對する確率統計的分析の試み / 師茂樹 ) Author(s) Citation (2004) Issue Date URL Right Typ
Title 中國宗教文獻研究國際シンポジウム報告書 ( 大規模佛教文獻群に對する確率統計的分析の試み / 師茂樹 ) Author(s) Citation (2004) Issue Date 2004-12 URL http://hdl.handle.net/2433/65875 Right Type Conference Paper Textversion publisher Kyoto University
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1 1 2,,.,.,,, SIFT.,,. Pitching Motion Analysis Using Image Processing Shinya Kasahara, 1 Issei Fujishiro 1 and Yoshio Ohno 2 At present, analysis of pitching motion from baseball videos is timeconsuming
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x-means 1 2 2 x-means, x-means k-means Bayesian Information Criterion BIC Watershed x-means Moving Object Extraction Using the Number of Clusters Determined by X-means Clustering Naoki Kubo, 1 Kousuke
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2,a) 2,b) 2,c) 2,d),e) WiFi WiFi WiFi 1. SNS GPS Twitter Facebook Twitter Ustream 1 Graduate School of Information Science and Technology, Osaka University, Japan 2 Cybermedia Center, Osaka University,