際際滷

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December 10, 2015, University Of Tsukuba, The 3Rd Area Building B Room #202
Supported ?by ? ?
JSPS ?Grant-\??in-\??Aid ?for ?Challenging ?Exploratory ?Research
ベイジアンゲ`ムモデルを?喘いた
スポ`ツシ`ンにおける佚廷廷戻?幣
弌直 巷賓椳 括望云 F岻
殕佚寄僥
及1指 階繁スポ`ツ僥g冩梢氏
匯違笥處セッション#2 スポ`ツの
もくじ
2
はじめに ?
ベイジアンゲ`ム ?
佚廷廷容協 ?
方タ箭 ?
おわりに
はじめに
3
スポ`ツとh廠の
?伉尖尖や湖秤を爺殲鵑澆燭い睦yできないか ?
娼舞議なO湫Bo彜Bでの栽(ゲ`ム尖尖モデル) ?
?返の?佩佩咾鰉yしながら?徭蛍の?佩佩咾Qめる(尸議) ?
?伉尖尖彜Bによって?佩佩咾笋錣襪もしれない(音音_かさ) ?
?伉尖尖や云?咄宗頴田酊遏? ?? 藺埖?羨羨宛Q蘿鵑覆
云k燕の?朕議
尸議かつ音音_かな吭房Q協和での佚廷廷麻 ?
スポ`ツシ`ン坤謄縫垢離稀`ビス ?
ゲ`ム尖尖のMみで佚廷廷(_楕楕楕)の麻 ?
階?繁スポ`ツに篠嚥する尖尖や室gのh
藺埖墅優鴬`ムモデルの撹勣殆 ?
プレイヤ坤稀`バ`レシ`バ ?
?佩佩咤坤轡腑奪?リタ`ンのN ?
?喘坤轡腑奪?リタ`ンの誼吭業業 ?
詞栽藺埖圍?佩佩喇呂隆_楕楕楕蛍下 ? ? ? ?, ? ?
協坤廛譽ぅ笋郎論軅躓漬睨Q協をする
藺墅優鴬`ム
4
藺埖墅優鴬`ムモデル坤謄縫垢離稀`ビス
1, 2 3, 1
0, 42, 1
flat
spin
flat spin
?a
?aa
as1(?a)
s1(a)
s2(a)s2(?a)
サ`バ`
レシ`バ
s1 s2
甚
佩
詞栽藺
紗えてプレイヤの?伉尖尖秤鵑凌] ?
?伉嶄ではフラット ?or ?スピンサ`ブ(タイプ)をQめる(佚廷廷) ?
gHにはフラット ?or ?スピンサ`ブを嬉つ(?佩佩)
ベイジアンゲ`ムモデル(弖紗蛍のみ) ?
タイプ(?伉嶄)坤侫薀奪 ?or ?スピン ?
佚廷廷坤織ぅ徂呂隆_楕楕楕蛍下 ?
協査論軅躓張廛譽ぅ
藺墅優戰ぅ献▲鵐鴬`ム
5
ベイジアンゲ`ムモデル坤謄縫垢離稀`ビス
2, 2 0, 1
3, 41, 1
flat
spin
flat spin
?a
?aa
a
1, 2 3, 1
0, 42, 1
flat
spin
flat spin
s1(a|?)s1(?a|?)
s2(?a|?)s2(a|?)
?a
?aa
a
flat ?
?2
flat?
?1
2, -1 0, -1
3, -11, -1
flat
spin
flat spin
s1(?a|??)s1(a|??)
?a
?aa
a
spin??
1 ?1
1, -1 3, -1
0, -12, -1
flat
spin
flat spin
s2(a|??) s2(?a|??)
?a
?aa
a
spin ??
1 ?2
タイプ佚廷
佚廷容協
6
佚廷廷の容協アルゴリズム(古勣)
佚廷廷容協} ?
譲財彜Bの詞栽藺埖圓Qyされプレイヤの佚廷廷を箔める ?
アイデア
[2] T. Suzuki and K. Kogiso, SICE International Symposium on Control Systems, 2016. (to appear)
[1] K. Kogiso, IEEE Conference on Decision and Control, 2015. (to appear)
譲財盾裂}[3] ?
プレイヤの佚廷廷が嚥えられ譲財彜Bになる詞栽藺埖圓鯒鵑瓩襭
譲財盾裂}と佚廷廷容協}のvS沙イい膨}
??(k + 1) = diag(A1, A2)??(k)
?s(k + 1) = A (ci(k))?si(k)
xx柊rg?掲侘r筌轡好謄[1]
Oパラメ`タ? ? と? ? のС
フィ`ドフォワ`ド崙囮狼O[2]
?
A1 A2
システムの?徭喇鬴陲林麻
[3] Y. Shoham and K. Leyton-Brown, Multiagent Systems, Cambridge University Press, 2009.
方タ
7
テニスのサ`ビス
2, 2 0, 1
3, 41, 1
flat
spin
flat spin
?a
?aa
a
1, 2 3, 1
0, 42, 1
flat
spin
flat spin
s1(a|?)s1(?a|?)
s2(?a|?)s2(a|?)
?a
?aa
a
flat ?
?2
flat?
?1
2, -1 0, -1
3, -11, -1
flat
spin
flat spin
s1(?a|??)s1(a|??)
?a
?aa
a
spin??
1 ?1
1, -1 3, -1
0, -12, -1
flat
spin
flat spin
s2(a|??) s2(?a|??)
?a
?aa
a
spin ??
1 ?2
75%
57% 95%
25%
75%
25%
43%  ?5%
26%
74%
52% 48%
盾h宀仝Aliceは74%でスピンサ`ブを粧いつつ75%の_楕楕楕でフラッ
トサ`ブを嬉つでしょう´々
おわりに
8
はじめに ?
ベイジアンゲ`ム ?
佚廷廷容協 ?
方タ箭 ?
おわりに

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