$30 off During Our Annual Pro Sale. View Details »
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
ハンカチ落としの戦略最適化
Search
Katsuki Ohto
July 07, 2020
Science
0
1.2k
ハンカチ落としの戦略最適化
漫画「嘘喰い」に登場するハンカチ落としゲームを簡略化してナッシュ均衡戦略を計算します。
Katsuki Ohto
July 07, 2020
Tweet
Share
More Decks by Katsuki Ohto
See All by Katsuki Ohto
負け側の残り枚数を最大化する二人単貧民の解析
yuricat
0
100
二人単貧民の消費枚数に関する勝利条件の一般化とその解析
yuricat
0
200
二人単貧民の定理を Coqで証明する試み
yuricat
0
210
Other Decks in Science
See All in Science
Hakonwa-Quaternion
hiranabe
1
160
サイコロで理解する原子核崩壊と拡散現象 〜単純化されたモデルで本質を理解する〜
syotasasaki593876
0
130
Vibecoding for Product Managers
ibknadedeji
0
120
20251212_LT忘年会_データサイエンス枠_新川.pdf
shinpsan
0
160
データマイニング - グラフ埋め込み入門
trycycle
PRO
1
130
AI(人工知能)の過去・現在・未来 —AIは人間を超えるのか—
tagtag
1
210
データから見る勝敗の法則 / The principle of victory discovered by science (open lecture in NSSU)
konakalab
1
250
データマイニング - グラフデータと経路
trycycle
PRO
1
260
HDC tutorial
michielstock
0
260
Rashomon at the Sound: Reconstructing all possible paleoearthquake histories in the Puget Lowland through topological search
cossatot
0
190
AI(人工知能)の過去・現在・未来 —AIは人間を超えるのか—
tagtag
0
130
【論文紹介】Is CLIP ideal? No. Can we fix it?Yes! 第65回 コンピュータビジョン勉強会@関東
shun6211
5
2.1k
Featured
See All Featured
Chrome DevTools: State of the Union 2024 - Debugging React & Beyond
addyosmani
9
1k
Sharpening the Axe: The Primacy of Toolmaking
bcantrill
46
2.6k
How To Stay Up To Date on Web Technology
chriscoyier
791
250k
[RailsConf 2023] Rails as a piece of cake
palkan
58
6.2k
SEO Brein meetup: CTRL+C is not how to scale international SEO
lindahogenes
0
2.2k
How to Ace a Technical Interview
jacobian
281
24k
A brief & incomplete history of UX Design for the World Wide Web: 1989–2019
jct
1
250
The Spectacular Lies of Maps
axbom
PRO
1
390
Easily Structure & Communicate Ideas using Wireframe
afnizarnur
194
17k
Neural Spatial Audio Processing for Sound Field Analysis and Control
skoyamalab
0
120
Reflections from 52 weeks, 52 projects
jeffersonlam
355
21k
A better future with KSS
kneath
240
18k
Transcript
ϋϯΧνམͱ͠ ͷઓུ࠷దԽ Katsuki Ohto Optimization Night #3 LT
ϋϯΧνམͱ͠ ➤ Ұൠతʹ… தఔͷਓͰߦ͏ ϨΫϦΤʔγϣϯήʔϜ ➤ ອըʮӕ͍ᷰʯಡऀʹ… ೋਓͰ໋ΛṌ͚ͯઓ͏ήʔϜ ϋϯΧνΛམͱ͢ํΛʮυϩοϓଆʯৼΓ͍ͯϋϯΧν͕མ ͪͨͷΛ֬ೝ͢ΔํΛʮνΣοΫଆʯͱ͠ɺަޓʹ୲͍ͯ͠
͘ɻਐߦʹ࣌ใΛར༻͢Δɻ1λʔϯ1ؒͱ͠ɺυϩοϓ ଆඞͣͦͷ࣌ؒʹམͱ͞ͳ͚ΕͳΒͣɺνΣοΫଆඞͣ Ұ͚ͩৼΓ͔ͳ͚ΕͳΒͳ͍ɻυϩοϓଆ͕ϋϯΧνΛ མͱͨ͠ॠ͔ؒΒνΣοΫଆͷʮ࠲ࢹͷࡍʯ͕ελʔτɺ༰ث ͷத֖͕։͖γϦϯμʔʹʮྟࢮༀʯ͕ཷ·͍ͬͯ͘ɻৼΓ͍ ͯϋϯΧν͕མ͍ͪͯΕνΣοΫޭͱͳΓத֖͕ด͡Δ͕ ٯʹམ͍ͪͯͳ͚ΕʮϖφϧςΟʯ͕ൃಈɻʮͦͷ࣌Ͱཷ ·͍ͬͯΔྟࢮༀʴ1ؒͰཷ·ΔྔʯΛͦͷͰࣹʢγϦϯ μʔʹྟࢮༀ͕5ؒཷ·ͬͨ߹ଈࣹʣ͞ΕΔɻͦͯ͠ ຺ഥ͕ࢭ·ͬͨͷΛ֬ೝ͔ͯ͠Βʮྟࢮʯ͕ελʔτɻϖφϧ ςΟඵΛফԽͨ͠ΒྟࢮༀͱରʹͳΔͷʮોੜༀʯΛ ্ࣹͨ͠Ͱ15ճݶఆͷ৺ଁϚοαʔδʢ10ඵؒ΄ͲʣΛߦ ͍ɺͦΕͰોੜͰ͖ͨΒήʔϜଓߦɺͰ͖ͳ͚Εউෛ͋Γɻ Wikipedia ʮӕ͍ᷰʯΑΓ
؆ུԽϧʔϧ ➤ υϩοϓଆ …ϋϯΧνΛམͱ͢ଆ ➤ νΣοΫଆ …ৼΓฦΔଆ ➤ ࣌ࠁ T
ඵؒ ➤ ϖφϧςΟʢ㲈ใुʣ ɾνΣοΫଆ͕མͱ͞Εͯ ɹ t ඵޙʹৼΓฦΔ… t ɾνΣοΫଆ͕ઌʹৼΓฦΔ ɹ… T ➤ ອըͰɺ͜ΕΛ෦ήʔϜͱͯ͠ ܁Γฦ͢ཁૉ͕͋Δ͕ɺ ࠓճ͜ͷҰճͷήʔϜ͚ͩߟ͑Δ
ಉ࣌ ήʔϜ ͷੑ࣭
͡ΌΜ͚Μ ➤ άʔΛग़͢ઓུʹ ˠύʔΛग़͢ઓུ͕༗ޮ ➤ ύʔΛग़͢ઓུʹ ˠνϣΩΛग़͢ઓུ͕༗ޮ ➤ νϣΩΛग़͢ઓུʹ ˠάʔΛग़͢ઓུ͕༗ޮ
➤ ઓུ͕॥͠ɺৗʹ࠷దͳ ઓུ͕ఆ·Βͳ͍ φογϡۉߧɹΛߟ͑Δ
φογϡۉߧઓུ ➤ ยํͷϓϨΠϠ͕͔ࣗΒख Λม͑ΔϝϦοτ͕ͳ͍ઓུ ʢͷΈ߹Θͤʣ ➤ ғޟকعͳΒউརखͲΕ͔ ҰͭΛબͿઓུͰOK ➤ ಉ࣌ήʔϜ
ɾ͡ΌΜ͚Μ ෆશใήʔϜ ɾϙʔΧʔɹɾຑ ͜ΕΒͷήʔϜͰ φογϡۉߧ֬తઓུ
ઓུ࠷ద Խ
తؔ ➤ ࣌ࠁ T+1 ·ͰԆ͠ɺνΣοΫଆɺυϩοϓଆ͕Կ͠ͳ͔ͬͨ߹ ࣌ࠁ T+1 ʹߦಈΛىͨ͜͜͠ͱʹ͢Δʢ݁ՌʹӨڹͳ͍ʣ ➤ ઓུ
࣌ࠁ i Ͱυϩοϓ͢Δ֬ ͨͩ͠ ࣌ࠁ j ͰνΣοΫ͢Δ֬ ͨͩ͠ ➤ ϖφϧςΟͷظ Di T+1 ∑ i=1 Di = 1 Cj T+1 ∑ j=1 Cj = 1 R(C, D) = T+1 ∑ i=1 Di ( i−1 ∑ j=1 Cj T + T+1 ∑ j=i Cj (j − i)) T=1ͷͱ͖ x = D1, y = C1ͱͯ͠
߆ଋ͖݅ͭͷఀཹ ➤ ϖφϧςΟͷظ ➤ φογϡۉߧͰɺνΣοΫଆɺυϩοϓଆ ͱʹઓུΛมߋ͢ΔΠϯηϯςΟϒ͕ͳ͍ ➤ →֬ͷ͕ 1ͱ͍͏ ɹ߆ଋ͖݅ͭͷఀཹ
➤ →ϥάϥϯδϡͷະఆ๏Λར༻͢Δ R(C, D) = T+1 ∑ i=1 Di ( i−1 ∑ j=1 Cj T + T+1 ∑ j=i Cj (j − i)) T=1ͷͱ͖ x = D1, y = C1ͱͯ͠
ϥάϥϯδϡͷະఆ๏ ➤ ཱࣜ ➤ ల։ ➤ ղऍ ͜ͷࣜ
͔ͭ ͱॻ͚Δ F = R(D, C) − γ( T+1 ∑ i=1 Di − 1) − λ( T+1 ∑ j=1 Cj − 1) ∂F ∂Dt = ∂F ∂Ct = ∂F ∂γ = ∂F ∂λ = 0 ∂F ∂Dt = t−1 ∑ j=1 Cj T + T+1 ∑ j=t Cj (j − t) − γ ∂F ∂Ct = t ∑ i=1 Di (t − i) + T+1 ∑ i=t+1 Di T − λ ∂R ∂Dt = const . ∂R ∂Ct = const .
νΣοΫଆͷԽࣜಋग़ ➤ υϩοϓଆͷ͔ࣜΒελʔτ ➤ ∂F ∂Dt =
0 = ∂F ∂Dt+1 t−1 ∑ j=1 Cj T + T+1 ∑ j=t Cj (j − t) − γ = t ∑ j=1 Cj T + T+1 ∑ j=t+1 Cj (j − t − 1) − γ 0 = Ct T − T+1 ∑ j=t+1 Cj Ct = ∑T+1 j=t+1 Cj T
υϩοϓଆͷԽࣜಋग़ ➤ νΣοΫଆͷ͔ࣜΒελʔτ ➤ ∂F ∂Ct =
0 = ∂F ∂Ct+1 t ∑ i=1 Di (t − i) + T+1 ∑ i=t+1 Di T − λ = t+1 ∑ i=1 Di (t + 1 − i) + T+1 ∑ i=t+2 Di T − λ Dt+1 T = t ∑ i=1 Di Dt+1 = ∑t i=1 Di T
ܭࢉ݁Ռ·ͱΊ ➤ ➤ ➤ ͜Ε͔Βͷ͔ࣜΒφογϡۉߧઓུ͕ఆ·Δ ➤ υϩοϓଆͱνΣοΫଆͰରশʹͳ͍ͬͯΔ ʢ͜͜ϖφϧςΟͷઃఆ࣍ୈʣ Dt+1
= ∑t i=1 Di T T+1 ∑ i=1 Di = 1 Ct = ∑T+1 j=t+1 Cj T T+1 ∑ i=1 Ci = 1
ઓུՄࢹ Խ
φογϡۉߧઓུ ➤ T = 10 ͷ߹Λਤࣔ ➤ υϩοϓଆʮ͙͢མͱ͢ʯ νΣοΫଆʮৼΓ͔ͣʯ ͷ͕֬Ұ൪ߴ͍
➤ ͦΕҎ֎Ͱ֬ΏΔ͔ ʹมԽ
࿈ଓ֦࣌ؒு ➤ T = 100Ͱͷ͚֬ͩԼ͕ Βͣɺ͋ͱ0ʹ͍͍ۙͮͯΔ ➤ ήʔϜΛ࣌ࠁ 0 ~
1 Ͱ࿈ଓత ʹ͢Δ֦ுΛߟ͑Δ ➤ ࿈ଓ֦࣌ؒுͰɺ υϩοϓଆʮ͙͢མͱ͢ʯ νΣοΫଆʮৼΓ͔ͣʯ ͷ֬ͷऩଋ ➤ ͦΕҎ֎Ͱ؇͔ͳ֬ີ ͕ఆ·Δ 1 e
͓ΘΓʹ ➤ ͡ΌΜ͚Μͱಉ͘͡ɺ φογϡۉߧઓུʹରͯ͠ઓུΛมԽͤͯ͞ɺ ϖφϧςΟͷظมԽͤͣɺฏۉҎ্উͭ͜ͱͳ͍ ➤ ͨͩ͠ɺφογϡۉߧΛ಄ʹೖΕ͓ͯ͘͜ͱͰɺ ઌʹࣗͷบΛόϥͣ͞ʹྫྷ੩ʹઓ͏͜ͱͰ͖Δ ➤ ࠓճ͕ࣜ؆୯ͰखܭࢉͰ͖͕ͨɺෳࡶͳ߹ػցͰ࠷దԽ͍ͯ͘͠
߹͋Δ ➤ ໋ΛṌ͚ͯʢṌ͚ͳͯ͘ʣ ϋϯΧνམͱ͠Ͱઓ͏߹ʹ φογϡۉߧͷ͜ͱࢥ͍ग़ͯ͠ཉ͍͠Ͱ͢ɻ