Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Sign up for free
Menu
Search
Features
All features
Private URLs
Password Protection
Custom URLS
Scheduled publishing
Remove Branding
Restrict embedding
Deck Collections
Notes
Features
All features
Private URLs
Password Protection
Custom URLS
Scheduled publishing
Remove Branding
Restrict embedding
Deck Collections
Notes
Explore
Featured decks
Featured speakers
Programming
Technology
Storyboards
Explore
Featured decks
Featured speakers
Programming
Technology
Storyboards
Pricing
Search
Sign in
Sign up for free
【NLPコロキウム】Stepwise Alignment for Constrained La...
Search
Akifumi Wachi
December 17, 2024
Research
850
3
Share
Embed
Copy iframe code
Copy JS code
Copy link
Start on current slide
【NLPコロキウム】Stepwise Alignment for Constrained Language Model Policy Optimization (NeurIPS 2024)
https://nlp-colloquium-jp.github.io/schedule/2024-12-18_akifumi-wachi/
Akifumi Wachi
December 17, 2024
More Decks by Akifumi Wachi
See All by Akifumi Wachi
[IBIS 2025] 深層基盤モデルのための強化学習驚きから理論にもとづく納得へ
akifumi_wachi
21
12k
JSAI NeurIPS 2024 参加報告会(AI アライメント)
akifumi_wachi
5
1.3k
Safe Reinforcement Learning - Guest Speaker Session at Cohere for AI
akifumi_wachi
0
340
NeurIPS-23 参加報告 + DPO 解説
akifumi_wachi
7
4.2k
Other Decks in Research
See All in Research
PHTalks Bengaluru - SSRF When All Else Fails
dk999
0
1.2k
Karkada さんの論文 × 2 の紹介: (1) Closed-Form Training Dynamics Reveal Learned Features and Linear Structure in Word2Vec-like Models, (2) Symmetry in language statistics shapes the geometry of model representations
eumesy
PRO
1
940
SAM3を用いたコマ・吹き出しの 領域検出と分割構造からの読み順推定
kzmssk
0
210
生成AIなんでも展示会vol6 LT登壇資料 NexteraBERT
rikkabotan7
0
210
2025年度秋葉原ウォーカブルプロジェクト調査報告 「アキバらしいウォーカブル」とは何か
izumiyama_lab
1
280
SPACE 2026 - Renforcer l’attractivité des métiers des productions animales dans les établissements d'enseignement agricole
institutdelelevage
PRO
0
120
La génomique au service de la fromageabilité du lait grâce aux spectres MIR
institutdelelevage
PRO
0
210
[IEICE-Soceity-Conf2026] セマンティック通信を見据えたマルチスケールセンシングと 学習の融合によるデジタルツイン基盤 / Digital Twin Infrastructure via the Fusion of Multi-Scale Sensing and Learning toward Semantic Communications
pman0214
0
140
[最先端NLP勉強会2026] Agentic Rubrics as Contextual Verifiers for SWE Agents
rfujii
1
410
Être éleveur dans un monde en transition : Comprendre les changements pour mieux les accompagner
institutdelelevage
PRO
0
160
Model Predictive Control for Uncertain Systems: Robust & Data-Driven Designs
kohlerjohannes
0
210
J-STAGEの現況と全文XML登載必須化について
xspa2012
0
380
Featured
See All Featured
State of Search Keynote: SEO is Dead Long Live SEO
ryanjones
0
350
Code Review Best Practice
trishagee
74
20k
Visualization
eitanlees
153
17k
SEOcharity - Dark patterns in SEO and UX: How to avoid them and build a more ethical web
sarafernandez
0
320
Put a Button on it: Removing Barriers to Going Fast.
kastner
60
4.6k
VelocityConf: Rendering Performance Case Studies
addyosmani
331
25k
How to optimise 3,500 product descriptions for ecommerce in one day using ChatGPT
katarinadahlin
PRO
3
3.9k
Product Roadmaps are Hard
iamctodd
55
13k
I Don’t Have Time: Getting Over the Fear to Launch Your Podcast
jcasabona
35
2.9k
Scaling GitHub
holman
464
140k
Tell your own story through comics
letsgokoyo
1
1.1k
Un-Boring Meetings
codingconduct
0
480
Transcript
4UFQXJTF"MJHONFOUGPS $POTUSBJOFE-BOHVBHF.PEFM 1PMJDZ0QUJNJ[BUJPO "LJGVNJ8BDIJ 5IJFO 25SBO 3FJ4BUP 5BLVNJ5BOBCF :PVIFJ "LJNPUP
݄ !/-1ίϩΩϜ 1 /FVS*14 IUUQTBSYJWPSHBCT
"LJGVNJ8BDIJʢ ྎྑʣ ܦྺ • r ɿ*#.౦ژجૅݚڀॴ 3FTFBSDI4DJFOUJTU • r ݱࡏɿ-*/&Ϡϑʔݚڀॴ
$IJFG3FTFBSDI4DJFOUJTU ݚڀ • ڧԽֶश ºʢ"*4BGFUZ ࣗવݴޠॲཧʣ ஶॻʢڞஶʣ • ʰڧԽֶश͔Β৴པͰ͖Δҙࢥܾఆʱ ओͳੜଉҬ • .-"*ܥͷֶձʢ/FVS*14 *$.- """* *+$"* FUDʣ ຊ͢༰ɺ/FVS*14Ͱൃද͖ͯͨ͠༰Ͱ͢ʂ 2
3 എܠɿݴޠϞσϧͷΞϥΠϝϯτ 3-)' • ݴޠϞσϧͷΞϥΠϝϯτͱʁ • ݴޠϞσϧΛਓؒͷՁ؍ඪʹ߹கͤ͞Δϓϩηε • 3-)' 3FJOGPSDFNFOU-FBSOJOHGSPN)VNBO'FFECBDL
<> ͕Α͘༻͍ΒΕΔ 0VZBOH 5SBJOJOHMBOHVBHFNPEFMTUPGPMMPXJOTUSVDUJPOTXJUIIVNBOGFFECBDL *O/FVS*14
4 3-)'ͷύΠϓϥΠϯ ˢ ڭࢣ͋Γֶश ʢ4'5ʣ ˢ 1SFGFSFODFEBUB ͰใुϞσϧΛֶश ˢ ֶशͨ͠ใुϞσϧ
Λ༻͍ͯڧԽֶश *NBHFUBLFOGSPN0VZBOH 1SFGFSFODFEBUBճͷ࣭Λਓ͕ؒൺֱɾϥϯΩϯάͨ͠σʔλͷ͜ͱ 4UFQ 4UFQ 4UFQ
5 3-)'ෳࡶɾෆ҆ఆ *NBHFUBLFOGSPN;IFOH ;IFOH 4FDSFUTPG3-)'JOMBSHFMBOHVBHFNPEFMTQBSU*110 BS9JW
QSFQSJOUBS9JW
%10%JSFDU1SFGFSFODF0QUJNJ[BUJPO • /FVS*14डจͷҰͭʢ0VUTUBOEJOH.BJO5SBDL3VOOFS6QTʣ 6 3BGBJMPW %JSFDU1SFGFSFODF0QUJNJ[BUJPO:PVS-BOHVBHF.PEFMJT4FDSFUMZB3FXBSE.PEFM *O/FVS*14 ਓೳֶձެࣜ
:PV5VCF Ͱղઆͯ͠·͢
• 3-)'ͷʮใुϞσϧͷֶशʯʴʮڧԽֶशʯΛ؆ུԽ͢Δ࠷దԽΛఏҊ • %10%JSFDU1SFGFSFODF0QUJNJ[BUJPO • ͳΜ͔ۙࣅͰͨ͠ΜͰ͔͢ʁ ˠ ͍͍͑ɺֶతʹՁͰ͢ 7 %10
= Ձ ใुϞσϧͷֶश ڧԽֶश ڭࢣ͋Γֶश ʢͬͪ͜ͷ΄͏͕ղ͖͍͢ʣ *NBHFUBLFOGSPN3BGBJMPW 3BGBJMPW %JSFDU1SFGFSFODF0QUJNJ[BUJPO:PVS-BOHVBHF.PEFMJT4FDSFUMZB3FXBSE.PEFM *O/FVS*14
8 ,50,BIOFNBO5WFSTLZ0QUJNJ[BUJPO • %10ͱಉ༷ʹɺ3-Λ༻͍ͣʹڭࢣ͋ΓֶशΛҰճղ͘ Ethayarajh et al. "KTO: Model alignment
as prospect theoretic optimization." arXiv preprint arXiv:2402.01306 (2024). ≻ 8JOOFS -PTFS • σʔληοτͷܗ͕ࣜҟͳΔ • 3-)' %10ˠ 1SFGFSFODFEBUB • ճ"ճ#ΑΓϕλʔ • ,50ˠ 6OQBJSFEͳೋσʔλ • ߴධՁɾධՁʢ:PV5VCFͳͲʣ • σʔληοτͷ࡞͕༰қ • σʔληοτͷܗࣜɾΞϧΰϦζϜ͕ଟछଟ༷ʹ • ධՁࢦඪσʔληοτʹΑͬͯɺదͳΞϧΰϦζϜ͕ҧ͏ 3-)'%10 ,50
9 3-)' %10 ,50Λମܥతʹཧղ͢Δ 3-)' ≻ 1SFGFSFODFEBUB ใुϞσϧ ΞϥΠϝϯτ ͞ΕͨݴޠϞσϧ
%10͕ొ͢Δ·Ͱɺσʔλ͔Β ΞϥΠϝϯτ͢ΔࣄͰ͖ͳ͔ͬͨ ˣ ใुϞσϧΛܦ༝ͱֶͯ͠श
10 3-)' %10 ,50Λମܥతʹཧղ͢Δ %10 ≻ 1SFGFSFODFEBUB ,50 ใुϞσϧ ΞϥΠϝϯτ
͞ΕͨݴޠϞσϧ ରԠؔΛղੳతʹಋग़ ܦ༝ͩͬͨใुϞσϧͷֶश͕ɺݴޠϞσϧͷΞϥΠϝϯτ ͱ͍͏࠷ऴΰʔϧͱ࣮࣭తʹಉ͡ʹͳͬͨʂ
11 ࠷దղͷ֎ܗಉ͡ 3-)' %10 ,50͕ղ͍͍ͯΔํࡦ࠷దԽಉ͡ ͜ͷͷ࠷దղ͕ղੳతʹಘΒΕΔ ʢ ਖ਼نԽͷͨΊͷؔʣ ղ͍͍ͯΔ͕ಉ͡ݶΓɺ࠷దղಉ͡ ಋग़ʹ͍ͭͯɺ࠷ޙϖʔδʹ
ิεϥΠυ͕͋Γ·͢
3-)' %10 ,50ͷܽͱʁ 12
13 3-)'%10,50ͷܽͱʁ ධՁࢦඪ͕ݸͰ͋Δ͜ͱ ճͷྑ͠ѱ͕͠εΧϥʔͰධՁ͞ΕΔ͜ͱ Ϧϯΰʢྛޝ<>ɺֶ໊ .BMVTEPNFTUJDB .BMVTQVNJMBʣͱ όϥՊϦϯΰଐͷམ༿ߴ ·ͨͦͷՌ࣮Ͱ͢ɻ "OTXFS
ՌͰ͢ɻ "OTXFS ≻ Ϧϯΰʹ͍ͭͯڭ͑ͯԼ͍͞ 1SPNQU
14 3-)'%10,50ͷܽͱʁ ධՁࢦඪ͕ݸͰ͋Δ͜ͱ ճͷྑ͠ѱ͕͠εΧϥʔͰධՁ͞ΕΔ͜ͱ Ϧϯΰʹ͍ͭͯڭ͑ͯԼ͍͞ 1SPNQU Ϧϯΰʢྛޝ<>ɺֶ໊ .BMVTEPNFTUJDB .BMVTQVNJMBʣͱ όϥՊϦϯΰଐͷམ༿ߴ
·ͨͦͷՌ࣮Ͱ͢ɻ ΞϥϯɾνϡʔϦϯά͕ɺ ੨ࢎԽ߹ΛϦϯΰʹృΓ ͘ͳͬͨ͞Ε͍ͯ·͢ɻ "OTXFS ՌͰ͢ɻ "OTXFS ≻ ≻ ༗༻ੑ ҆શੑ
15 ݴޠϞσϧͷ҆શੑͱʁ ࡢࠓɺ4BGFUZ 5SVTUXPSUIJOFTTͱ͍͏໊ͷͱͰΜʹݚڀ ʮ҆શੑʯͱݴ༷ͬͯʑͳ֓೦ΛؚΉ ༗ൃݴɿݴɾੑతൃݴɾࠩผൃݴ FUD όΠΞε • ࠃ੶ɾੑผɾ࣏తࢤʹؔ͢ΔόΠΞε
• όΠΞεʢ͍จষΛΉʣ • ࣗݾධՁόΠΞεʢ͕ࣗੜ͢ΔจষͦΕʹࣅͨจষΛߴ͘ධՁ͢Δʣ ϓϥΠόγʔ • ݸਓใʢ༗໊ਓͷॅॴͳͲʣΛग़ྗͯ͠͠·͏ɺͳͲͳͲ
16 ҆શੑ੍͖ͷΞϥΠϝϯτ ௨ৗͷ 3-)'%10͕ղ͍͍ͯΔ࠷దԽ max s.t. max ˢ ଟछଟ༷ͳධՁࢦඪΛҰ࣍ݩͷใुؔ ʹԡ͠ࠐΊΔඞཁ͕͋Δ
ຊݚڀ͕ղ͘࠷దԽ ˢ ҆શੑʹؔ͢Δ੍݅ʢෳͰ0,ʣ ˢ લ෦ڞ௨
17 طଘݚڀɿ4BGF3-)' %BJFUBM4BGF3-)'4BGF3FJOGPSDFNFOU-FBSOJOHGSPN)VNBO'FFECBDL *O*$-3 NBYJNVN MJLFMJIPPE NBYJNVN MJLFMJIPPE GJOBM -.QPMJDZ
SFXBSENPEFM TBGFUZNPEFM MBCFMSFXBSE BOETBGFUZ TBNQMF DPNQMFUJPO 4BGF3-)' SFXBSE EBUB TBGFUZ EBUB 110-BHSBOHJBO ௨ৗͷ 3-)'Λૉʹ੍͖ʹ֦ு • 3FXBSENPEFM𝑟 ͱ TBGFUZNPEFM𝑔 ΛͦΕͧΕֶश • ͦͷޙϥάϥϯδϡ 𝜆 Λಋೖͯ͠ɺ 𝑟 + 𝜆𝑔 ͱ͍͏ؔʹؔͯ͠ 3-)' • ݴޠϞσϧํࡦ Кͱ ϥάϥϯδϡ 𝜆 Λಉ࣌ʹ࠷దԽ ͨͩͰ͑͞ෳࡶͳ3-)'͕͞ΒʹෳࡶԽ max s.t. ղ͘࠷దԽಉ͡
18 طଘݚڀɿ4BGF3-)' max s.t. ղ͘࠷దԽಉ͡ %BJFUBM4BGF3-)'4BGF3FJOGPSDFNFOU-FBSOJOHGSPN)VNBO'FFECBDL *O*$-3 NBYJNVN MJLFMJIPPE NBYJNVN
MJLFMJIPPE GJOBM -.QPMJDZ SFXBSENPEFM TBGFUZNPEFM MBCFMSFXBSE BOETBGFUZ TBNQMF DPNQMFUJPO 4BGF3-)' SFXBSE EBUB TBGFUZ EBUB 110-BHSBOHJBO ௨ৗͷ 3-)'Λૉʹ੍͖ʹ֦ு • 3FXBSENPEFM𝑟 ͱ TBGFUZNPEFM𝑔 ΛͦΕͧΕֶश • ͦͷޙϥάϥϯδϡ 𝜆 Λಋೖͯ͠ɺ 𝑟 + 𝜆𝑔 ͱ͍͏ؔʹؔͯ͠ 3-)' • ݴޠϞσϧํࡦ Кͱ ϥάϥϯδϡ 𝜆 Λಉ࣌ʹ࠷దԽ ͨͩͰ͑͞ෳࡶͳ3-)'͕͞ΒʹෳࡶԽ ͜ΕΛγϯϓϧͳํ๏Ͱ؆ུԽ͠·ͨ͠Αʂ ͱ͍͏ͷ͕ຊݚڀͷҰ൪ͷߩݙ ͔͠ཧతʹਖ਼Խ͞Ε͍ͯΔํ๏Ͱ ࣮ݧతʹΑ͘ಈ͘ʂ
19 ఏҊख๏ɿ4"$10 NBYJNVN MJLFMJIPPE NBYJNVN MJLFMJIPPE GJOBM -.QPMJDZ SFXBSENPEFM TBGFUZNPEFM
MBCFMSFXBSE BOETBGFUZ TBNQMF DPNQMFUJPO 4BGF3-)' 4"$10 SFXBSE EBUB TBGFUZ EBUB 110-BHSBOHJBO SFXBSE EBUB TBGFUZ EBUB NBYJNVN MJLFMJIPPE FH %10 ,50 SFGFSFODF -.1PMJDZ NBYJNVN MJLFMJIPPE FH %10 ,50 GJOBM -.1PMJDZ SFXBSEBMJHOFE -.1PMJDZ • 4"$104UFQXJTF"MJHONFOUGPS$POTUSBJOFE-BOHVBHF1PMJDZ0QUJNJ[BUJPO • ෳࡶͩͬͨ 4BGF3-)'͕ɺ%10 ,50Λஈ֊తʹճ͚ͩ͢ͷγϯϓϧͳͷͱͳͬͨ • ֶతʹՁͳͷͰɺ͜ͷૢ࡞ཧతʹਖ਼Խ͞Ε͍ͯΔ • ֤ΞϥΠϝϯτͰ͖ͳΞϧΰϦζϜʢ%10 ,50ʣΛͬͯཧతʹ0,
20 ஈ֊తͳΞϥΠϝϯτͷਖ਼ੑ max s.t. ຊݚڀͷ࠷దԽ ຊݚڀͷ࠷ద-.ํࡦ ɺҎԼͷؔΛຬͨ͢ ࠷దͳϥάϥϯδϡ 𝜆⋆Ͱɺ ใुͱ҆શੑΛॏΈ
˞ݫີͳূ໌จΛ͝ཡ͍͚ͨͩΔͱ͍Ͱ͢ɻ
21 ஈ֊తͳΞϥΠϝϯτͷਖ਼ੑ ใुʹؔͯ͠ ΞϥΠϝϯτ͞Εͨ-.ํࡦ ҆શؔ max s.t. ຊݚڀͷ࠷దԽ ຊݚڀͷ࠷ద-.ํࡦ ɺҎԼͷؔΛຬͨ͢
ஈ֊తͳΞϥΠϝϯτ͕ਖ਼Խ͞Ε͍ͯΔʂॱ൪ٯͰ 0,
22 4"$10ͷϝϦοτ %10 ≻ 1SFGFSFODFEBUB ,50 ใुϞσϧ ΞϥΠϝϯτ ͞ΕͨݴޠϞσϧ 4"$10ͷ֤εςοϓͰ৭ʑͳΞϧΰϦζϜͷબࢶ͕͋Δʂ
ใुʢ༗༻ੑʣ ,50ɾ҆શੑ %10ͱ͔ 0,ʂ ΞϧΰϦζϜͷॊೈੑ ˠ σʔληοτͷॊೈੑ
23 4"$10ͷ • 4"$10ɺ·ͩҰݸେ͖ͳ՝͕͋Δ • ༗༻ੑʹؔͯ͠ΞϥΠϝϯτͨ͠ޙɺ͞Βʹ҆શੑʹؔͯ͠ΞϥΠϝϯτ͢Δঢ়گΛߟ͑Δ ใुʢ༗༻ੑʣ ʹؔ͢Δσʔληοτ ҆શੑʹؔ͢Δ σʔληοτ
ΞϥΠϝϯτલ ͷݴޠϞσϧ ༗༻ੑͱ҆શੑ྆ํʹؔͯ͠ ΞϥΠϝϯτͨ͠ ݴޠϞσϧ ༗༻ੑʹؔͯ͠ ΞϥΠϝϯτͨ͠ ݴޠϞσϧ ༗༻ੑͱ҆શੑΛόϥϯε ͤ͞ΔͨΊͷύϥϝʔλ 𝝀
24 4"$10ͷ • φΠʔϒͳղ๏ɿʮЕߋ৽ ˠ ํࡦ࠷దԽʯΛ܁Γฦ͢ • ݴޠϞσϧͷΞϥΠϝϯτͷ߹ɺʮЕߋ৽ ˠ ํࡦ࠷దԽʯԿͨ͘͠ͳ͍ʂ
• ֶश͕࣌ؒେɾํࡦͷධՁ͕ෆ҆ఆ͔ͭߴίετ ใुʢ༗༻ੑʣ ʹؔ͢Δσʔληοτ ҆શੑʹؔ͢Δ σʔληοτ ΞϥΠϝϯτલ ͷݴޠϞσϧ ༗༻ੑͱ҆શੑ྆ํʹؔͯ͠ ΞϥΠϝϯτͨ͠ ݴޠϞσϧ ༗༻ੑʹؔͯ͠ ΞϥΠϝϯτͨ͠ ݴޠϞσϧ ༗༻ੑͱ҆શੑΛόϥϯε ͤ͞ΔͨΊͷύϥϝʔλ 𝝀
ઉա͗ͯൃݴ ͨ·ʹͪ͠Ό͏ େ͖Ίͷ 𝜆 Ͱ ΞϥΠϝϯτ 25 ࣮༻తͳ4"$10ʢ14"$10ʣ ༗༻ੑʹؔͯ͠ͷΈ ΞϥΠϝϯτͨ͠
ݴޠϞσϧ ҆શੑʹؔͯ͠อकత ʹ࠶ͼΞϥΠϝϯτ ͨ͠ݴޠϞσϧ ઢܗͷϞσϧϚʔδ ʢϞσϧͷॏΈΛ͚ͩ͢ʣ ΄ͲΑ҆͘શੑΛ ߟྀͨ͠Ϟσϧ ໓ଟʹൃݴ͠ͳ͍͚ Ͳɺޱ͕গͳ͗͢Δ ࠞ߹ׂ߹Λௐ͢Δ͜ͱʹ Αͬͯɺ҆શੑΛ੍ޚ͢Δʂ
26 ࣮ݧ݁Ռ • 4BGF3-)'ʢ࠷ॏཁͳطଘݚڀʣͱൺֱ • 4'5Ϟσϧɿ"MQBDBC σʔληοτɿ1,64BGF3-)', • ධՁࢦඪ •
3FXBSE ༗༻ͳจষΛग़ྗͰ͖Δ͔ 4BGFUZ ༗ͳจষΛग़ྗ͠ͳ͍͔ • ྫ͑ 4'5Ϟσϧ࠷ॳˣͷΑ͏ͳײ͡ɻ • ͜ͷϞσϧΛɺ༗༻ੑɾ҆શੑͷόϥϯεΛऔΓͳ͕Βɺ͍͔ʹ্खʹΞϥΠϝϯτ͢Δ͔Λڝ͏ %PYJOHͷํ๏Λϖϥϖϥ ڭ͑ͯ͠·͍ͬͯΔ
27 ࣮ݧ݁Ռʢ8JOSBUFWT4'5Ϟσϧʣ • ))FMQGVMOFTT 44BGFUZ
28 ࣮ݧ݁Ռʢ8JOSBUFWT4'5Ϟσϧʣ • ))FMQGVMOFTT 44BGFUZ • ࣈɿЌЕʢখ͍͞΄Ͳ҆શੑॏࢹʣ • %10 )
ˠ %10 4 ͱ ,50 ) ˠ %10 4 4BGF3-)'ΑΓ༗༻ੑɾ҆શੑͷ໘Ͱߴੑೳ • %10 ) ˠ ,50 4 ͷੑೳ͕͍ͷಾ • ,50҆શੑʹؔ͢ΔΞϥΠϝϯτͱ૬ੑ͕ѱ͍ʁ
࣮ݧ݁Ռʢ8JOSBUFWT4'5Ϟσϧʣ • ))FMQGVMOFTT 44BGFUZ • ΞϥΠϝϯτͷॱ൪ΛೖΕସ͑ • %10 4 ˠ
%10 ) ͱ %10 ) ˠ %10 4 ͕ ಉͷੑೳ • ࣮ཧͱ߹͕औΕ͍ͯΔ 29
30 ࣮ݧ݁Ռʢ8JOSBUFWT4'5Ϟσϧʣ • ))FMQGVMOFTT 44BGFUZ • ࣈɿϞσϧϚʔδͷׂ߹ʢେ͖͍΄Ͳ҆શੑॏࢹʣ • /BÏWF%10 )
ͱ %10 4 ΛϚʔδ • 14"$10ɺ%10 ) ͱ %10 ) ˠ %10 4 ΛϚʔδ • %10 ) ˠ %10 4 աʹ҆શʢʣ
31 ࣮ݧ݁Ռʢ࣮ࡍͷੜʣ <ΞϥΠϝϯτલ> %PYJOHͷํ๏Λϖϥϖϥ ڭ͑ͯ͠·͍ͬͯΔ <ΞϥΠϝϯτޙ> %PYJOHͷྙཧతΛ ٞͯ͠ஸॏʹஅ͍ͬͯΔ
32 ·ͱΊɿ5BLF)PNF.FTTBHFT • ධՁࢦඪͷҟͳΔෳͷσʔληοτ͕͋Δͱ͢Δ • ͦΕͧΕͷσʔληοτΛ༻͍ͯ %10 ,50Ͱஈ֊తʹద༻͢Δͷɺ ཧతʹਖ਼͍͠ %BUBTFU
SFGFSFODF -. "MJHOFE-.ᶃ "MJHOFE-.ᶄ %BUBTFU 𝑓" 𝑓# • Ξϊςʔλʔ͕જࡏతʹͭ ؔ 𝑓& ͱ 𝑓' ͷઢܗʹ ؔ͢ΔΞϥΠϝϯτʹ૬ • ؔ 𝑓& ͱ 𝑓' Λɺ𝛽' ɿ𝛽& ͷ ׂ߹ͰॏΈ͚ • ύϥϝʔλͷௐ͕େมͳͱ ͖ϞσϧϚʔδ͕ʹཱͭ 𝛽" 𝛽#
33 ิʢ̍ʣ ,-ͷఆٛ max{𝑋 − 𝛽𝑌} = min{Y − X/𝛽}ʢ𝛽
> 0ʣ MPHͱ FYQͷؔ log 𝑋 1/𝑍 − log 𝑍 = log 𝑋 =
34 ิʢ̎ʣ લϖʔδͷଓ͖ = ,-ͷఆٛ = 𝑍 𝑥 ͷΈʹґଘ͢Δؔ
ͳͷͰ min ! ʹؔͳ͠ Ϊϒεͷෆ͔ࣜΒ ,-Λ࠷খԽ͢Δ 𝜋 𝜋 = 𝜋∗ 𝜋∗ ͷఆٛ