変化検出と要約データ構造を用いた利用者の嗜好の変化に迅速に追従する多腕バンディット手法/iots2020-adaptive-linear-mab

第13回インターネットと運用技術シンポジウム（IOTS 2020)
https://www.iot.ipsj.or.jp/symposium/iots2020-program/

Transcript

1. ࡾ୐ ༔հ1,2), ܀ྛ ݈ଠ࿠1)
   1. Pepabo R&D Institute, GMO Pepabo, Inc., 2. ۝भେֶ େֶӃγεςϜ৘ใՊֶ෎ ৘ใ஌ೳ޻ֶઐ߈
   2020.12.03 ୈ13ճ Πϯλʔωοτͱӡ༻ٕज़γϯϙδ΢ϜʢIOTS 2020ʣ
   มԽݕग़ͱཁ໿σʔλߏ଄Λ༻͍ͨ
   ར༻ऀͷᅂ޷ͷมԽʹਝ଎ʹ௥ै͢Δ
   ଟ࿹όϯσΟοτख๏
   

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2. 1. ͸͡Ίʹ
   2. ؔ࿈ݚڀ
   3. ఏҊख๏
   4. ධՁ
   5. ·ͱΊ
   2
   ໨࣍
   

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3. 1.
   ͸͡Ίʹ
   

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4. • WebαʔϏεʹ͓͚Δ৘ใաଟ໰୊Λղܾ͢ΔɺਪનγεςϜͷಋೖ
   • → ͳΜΒ͔ͷํࡦʹج͖ͮଟ਺ͷબ୒ࢶ͔Βར༻ऀ͕ڵຯΛ࣋ͭ΋ͷΛఏ
   Ҋ͢ΔγεςϜ
   4
   എܠ
   • ঎඼
   • ޿ࠂ
   • ਪનΞϧΰϦζϜ
   

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5. • WebαʔϏεʹ͓͚Δ৘ใաଟ໰୊Λղܾ͢ΔɺਪનγεςϜͷಋೖ
   • → ͳΜΒ͔ͷํࡦʹج͖ͮଟ਺ͷબ୒ࢶ͔Βར༻ऀ͕ڵຯΛ࣋ͭ΋ͷΛఏ
   Ҋ͢ΔγεςϜ
   5
   എܠ
   • γεςϜʹͱͬͯར༻ऀͷᅂ޷͸ະ஌ʢਪଌͷͨΊͷ৘ใ஝ੵ͕ඞཁʣ
   • ͋Δ࣌఺Ͱ༗༻ͱߟ͑ΒΕΔ৘ใΛʮ׆༻ʯͨ͠ఏҊΛߦ͍ͭͭɺΑΓ༗༻ͳ
   ఏҊʹͭͳ͕Δ৘ใͷʮ୳ࡧʯ͕ٻΊΒΕΔʢػձଛࣦͷճආʣ
   ӡ༻্ͷ՝୊
   

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6. • ͋Δ࣌఺ʹ͓͚Δ࠷ળͳબ୒ͷͨΊɺ׆༻ͱ୳ࡧͷτϨʔυΦϑΛղܾ͍ͨ͠
   • → ଟ࿹όϯσΟοτ໰୊ͱΈͳͯ͠ɺಉ໰୊ͷղ๏Λద༻[1]
   6
   ݚڀͷ໨త
   <>ࡾ୐༔հ ็߃ݑ 4ZOBQTFจ຺ʹԠͯ͡ܧଓతʹਪનख๏ͷબ୒Λ࠷దԽ͢ΔਪનγεςϜ ిࢠ৘ใ௨৴ֶձ࿦จࢽ%
   7PM+% /P QQ /PW
   

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7. • ͋Δ࣌఺ʹ͓͚Δ࠷ળͳબ୒ͷͨΊɺ׆༻ͱ୳ࡧͷτϨʔυΦϑΛղܾ͍ͨ͠
   • → ଟ࿹όϯσΟοτ໰୊ͱΈͳͯ͠ɺಉ໰୊ͷղ๏Λద༻
   7
   ݚڀͷ໨త
   • ҰํͰɺैདྷͷಉ໰୊ͷղ๏Ͱ͸ɺར༻ऀͷᅂ޷͕ʮଟ༷͔ͭܧଓతʹมԽʯ
   ͢ΔΑ͏ͳ؀ڥʹॆ෼ʹରԠɾ௥ै͢Δ͜ͱ͕Ͱ͖ͳ͍ʢؔ࿈ݚڀͰઆ໌ʣ
   • ͜ͷ؀ڥʹରԠՄೳͳղ๏ΛఏҊ͢Δ͜ͱͰɺར༻ऀͷᅂ޷ͷଟ༷ੑ΍มԽʹ
   ௥ै͢ΔఏҊΛՄೳʹ͍ͨ͠
   

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8. 2.
   ؔ࿈ݚڀ
   

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9. • ʮ࿹ʯͱݺ͹ΕΔෳ਺ͷީิ͔ΒಘΒΕΔใुΛ࠷େԽ͢Δ໰୊
   • ϓϨΠϠʔ͸Ұ౓ͷࢼߦͰ1ͭͷ࿹Λબ୒͠ɺใुΛಘΔ
   • ͦΕͧΕͷ࿹͸͋Δใु෼෍ʹै͍ใुΛੜ੒
   • ͨͩ͠ɺϓϨΠϠʔ͸͜ͷใु෼෍Λࢼߦͷ݁Ռ͔Βਪଌ͢Δඞཁ͕͋Δ
   9
   ଟ࿹όϯσΟοτ໰୊
   • ϓϨΠϠʔ͸͋Δ࣌఺ͷ࿹ͷධՁʹج͖ͮʮ׆༻ʯͱʮ୳ࡧʯΛฒߦͯ͠ߦ͏
   • ͜ͷτϨʔυΦϑΛղফ͢ΔͨΊʹ༷ʑͳղ๏͕ఏҊ͞Ε͍ͯΔ
   

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10. ଟ࿹όϯσΟοτ໰୊ͷ૝ఆ͢Δ࿹ͷ֬཰෼෍ͷछྨ
    10
    Arm0
    Arm1
    Arm2
    User(s) System
    ਪఆͨ֬͠཰෼෍
    ਅͷ֬཰෼෍
    Recommend
    Click
    

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11. • ࿹͝ͱͷใु෼෍͸ৗʹಉ͡Ͱ͋Δͱ͍͏Ծఆ
    • → ঢ়گ΍ଐੑ͝ͱʹใु෼෍͕ҟͳΔͷͰ͸ͳ͍͔ʁ
    • ྫʣ೥୅͝ͱʹਓؾͷ঎඼͕ҧ͏ɺ࠷ۙɺಉ͡ΧςΰϦͷ঎඼Λങͬͨ
    • → ࣌ؒͷܦաʹΑͬͯ΋ใु෼෍͕มԽ͢ΔͷͰ͸ͳ͍͔ʁ
    • ྫʣ৽͍͠χϡʔεهࣄɺҰ࣌తͳྲྀߦ
    11
    ଟ࿹όϯσΟοτ໰୊ͷ֦ு
    • ʮઢܗʯ·ͨ͸ʮඇఆৗʯͳଟ࿹όϯσΟοτ໰୊ͱ֦ͯ͠ு͕ߦΘΕ͍ͯΔ
    

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12. • ࿹͝ͱʹෳ਺ͷจ຺͕͋Γɺจ຺ʹԠͯ͡ใु෼෍͕ܾ·Δଟ࿹όϯσΟοτ
    ໰୊ͷઃఆ
    • ຊݚڀใࠂͰ͸ɺจ຺͸ɺෳ਺ͷཁҼͷύϥϝʔλͷ૊Έ߹ΘͤͰදݱ͞
    Εͨঢ়ଶͷ͜ͱΛࢦ͢
    • → ཁҼύϥϝʔλͷ஋͕{0,1}ͷ৔߹ɺจ຺͸ཁҼ਺ ʹରͯ͠ ύλʔϯ
    d 2d
    12
    ઢܗͳଟ࿹όϯσΟοτ໰୊
    • ઢܗͳଟ࿹όϯσΟοτ໰୊ͷղ๏Ͱ͸ɺจ຺ͷ֬཰෼෍Ͱ͸ͳ͘ɺཁҼ͝ͱ
    ͷ܎਺ʢઢܗύϥϝʔλʣΛਪఆ͢Δ͜ͱͰ֤จ຺ʹ͓͚ΔใुΛ༧૝͢Δ
    

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13. ઢܗͳଟ࿹όϯσΟοτ໰୊
    13
    Arm0
    Arm1
    Arm2
    User(s) System
    ਪఆͨ֬͠཰෼෍
    ਅͷ֬཰෼෍
    Recommend
    Click
    Context = 0 Context = 0
    

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14. ઢܗͳଟ࿹όϯσΟοτ໰୊
    14
    Arm0
    Arm1
    Arm2
    User(s) System
    ਪఆͨ֬͠཰෼෍
    ਅͷ֬཰෼෍
    Recommend
    Click
    Context = 1 Context = 1
    

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15. • ಉ͡จ຺ʹ͓͍ͯ΋࣌ؒܦաʹΑͬͯใु෼෍͕มԽ͢Δଟ࿹όϯσΟοτ໰
    ୊ͷ໰୊ઃఆ
    • पظతͳมԽͰ͋Ε͹ཁҼͷύϥϝʔλʹؚΊΔ͜ͱͰରԠͰ͖Δ͕ෆن
    ଇͳ৔߹ʢඇఆৗͳมԽͷ৔߹ʣ͸͜ͷݶΓͰ͸ͳ͍
    15
    ඇఆৗͳଟ࿹όϯσΟοτ໰୊
    • ඇఆৗͳଟ࿹όϯσΟοτ໰୊ͷղ๏Ͱ͸ɺաڈʹ؍ଌͨ͠ใुʹଊΘΕͣ࿹
    ͷධՁΛਝ଎ʹߋ৽͢Δ͜ͱͰ֤จ຺ʹ͓͚ΔใुΛ༧૝͢Δ
    ׂҾܕΞϓϩʔν มԽݕग़ܕΞϓϩʔν
    

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16. ඇఆৗͳଟ࿹όϯσΟοτ໰୊
    16
    Arm0
    Arm1
    Arm2
    User(s) System
    ਪఆͨ֬͠཰෼෍
    ਅͷ֬཰෼෍
    Recommend
    Click
    t = 0~ t = 100~ t = 0~ t = 100~
    t = 99 t = 99
    

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17. ඇఆৗͳଟ࿹όϯσΟοτ໰୊
    17
    Arm0
    Arm1
    Arm2
    User(s) System
    ਪఆͨ֬͠཰෼෍
    ਅͷ֬཰෼෍
    Recommend
    Click
    t = 0~ t = 100~ t = 0~ t = 100~
    t = 199 t = 199
    

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18. • ࿹ͷใु෼෍ͷมԽΛલఏʹɺܧଓతʹ࿹ͷධՁΛߋ৽͢ΔΞϓϩʔν
    • աڈͷࢼߦճ਺ɺใुʹରׂͯ͠Ҿ཰Λಋೖ
    • → ৽͍͠؍ଌ݁ՌΛॏཁࢹ
    • UCB1΍Thomson SamplingΛ֦ுͨ͠ղ๏͕ఏҊ͞Ε͍ͯΔ
    • Discounted UCB, Sliding Window UCB
    • Dynamic Thompson Sampling, Discounted TS
    18
    ඇఆৗͳଟ࿹όϯσΟοτ໰୊ͷղ๏ - ׂҾܕ
    ✓
    Trialt Trialt 1
    · · · Trialt n
    Rewardt Rewardt 1
    · · · Rewardt n
    ◆
    0
    B
    B
    B
    @
    ↵1
    ↵2
    .
    .
    .
    ↵n
    1
    C
    C
    C
    A
    AAADbHichVHNbtNAEB7H0BYDbfg5IFVIUaNG5dBoHSoVcarEhQtSmzZtUV2i9WaTrLpZW+tNUDB+AV6AAyeQOCAegAfgwgtw6BMghMSllXrpgbFjCDRQxrL3m2/2m/3W44dSRIaQQ6tgX7g4NT1zybl85ersXPHa9e0o6GvGGyyQgd71acSlULxhhJF8N9Sc9nzJd/yDB2l9Z8B1JAK1ZYYh3+/RjhJtwahBqln84kneNkuO5/OOUDHVmg6TWGIkzpYWVDZjk5QqpZ942U0zj7UCE/1Oq8TznDp/SnUrV/xKzkjGvEocj6tWfqjjadHpmjvOXx0xrFMZdukTFw/KYS2Fg7TvmFMpnOzaLJZJlWRRmgRuDsqQx3pQ/AAetCAABn3oAQcFBrEEChE+e+ACgRC5fYiR04hEVueQgIPaPu7iuIMie4DfDmZ7OaswT3tGmZrhKRJfjcoSLJLP5B05Ip/Ie/KVnP6zV5z1SL0McfVHWh42517c2jz5r6qHq4HuWHWuZwNtuJd5Feg9zJj0FmykHzx7ebR5v74YV8gb8g39vyaH5CPeQA2O2dsNXn91jh8fveAfwwG5Z8cxCbZrVfdutbaxUl57nI9qBuZhAZZwHquwBg9hHRrArEdWZD23ksJ3+6Y9b98ebS1YueYG/BF25QcNWuOW
    

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19. • ࿹ͷใु෼෍ͷมԽΛܖػʹɺ࿹Λ࠶ධՁ͢ΔΞϓϩʔν
    • ᶃ ؍ଌͨ͠ใुΛ࣌ܥྻσʔλͱΈͳ͠ɺ౎౓ɺมԽݕग़ΛࢼΈΔ
    • ᶄ มԽΛݕग़ͨ͠৔߹ɺมԽޙͷࢼߦճ਺ɺใुͰ࿹ͷධՁΛߋ৽
    • มԽݕग़͸طଘͷख๏Λར༻ՄೳʢPage-Hinkley test, ADWINʣ
    • UCB1΍Thomson SamplingͱมԽݕग़Λ૊Έ߹Θͤͨղ๏͕ఏҊ͞Ε͍ͯΔ
    • Adapt-EvE, S-TS-ADWIN
    19
    ඇఆৗͳଟ࿹όϯσΟοτ໰୊ͷղ๏ - มԽݕग़ܕ
    ✓
    Trialt Trialt 1
    · · · Trialt n
    Rewardt Rewardt 1
    · · · Rewardt n
    ◆
    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
    มԽલ
    มԽޙ
    

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20. 3.
    ఏҊख๏
    

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21. • ଟ༷͔ͭܧଓతʹมԽ͢Δ؀ڥΛલఏͱ͍ͯ͠ͳ͍͔ɺ௥ैੑ͕े෼Ͱ͸ͳ͍
    21
    ैདྷख๏ͷ՝୊
    ઢܗʢෳ਺ͷจ຺ʣ ඇఆৗ
    จ຺
    ୯Ұ ෳ਺
    ใु෼෍ ఆৗ ε-Greedy
    UCB1
    Thompson Sampling
    LinUCB
    Linear Thompson Sampling
    ඇఆৗ ׂҾܕ Discounted UCB
    Sliding-window UCB
    Dynamic Thompson Sampling
    Discounted TS
    Decay LinUCB
    มԽݕग़ܕ Adapt-EvE
    S-TS-ADWIN
    

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22. จ຺
    ୯Ұ ෳ਺
    ใु෼෍ ఆৗ ε-Greedy
    UCB1
    Thompson Sampling
    LinUCB
    Linear Thompson Sampling
    ඇఆৗ ׂҾܕ Discounted UCB
    Sliding-window UCB
    Dynamic Thompson Sampling
    Discounted TS
    Decay LinUCB
    มԽݕग़ܕ Adapt-EvE
    S-TS-ADWIN
    Adaptive-Linear-MAB
    • ଟ༷͔ͭܧଓతʹมԽ͢Δ؀ڥΛલఏͱ͍ͯ͠ͳ͍͔ɺ௥ैੑ͕े෼Ͱ͸ͳ͍
    • → ఏҊख๏Ͱ͸ઢܗͳख๏ͱඇఆৗͳख๏Λ૊Έ߹ΘͤΔ͜ͱͰରԠ
    22
    ैདྷख๏ͷ՝୊
    

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23. • ඇఆৗͳଟ࿹όϯσΟοτ໰୊ͷղ๏Λઢܗʹ֦ு
    • → ैདྷख๏Λ൚༻తʹར༻Ͱ͖ɺׂҾܕΞϓϩʔνͱൺֱͯ͠΋ྑ͍ධՁ
    ͕ಘΒΕ͍ͯΔɺมԽݕग़ܕΞϓϩʔνͰ͋ΔS-TS-ADWIN[2]ͷ֦ு
    23
    ఏҊख๏
    <>&EPVBSE'PVDI
    F +VOQFJ,PNJZBNB BOE,MFNFOT#P
    „IN4DBMJOHNVMUJBSNFECBOEJUBMHPSJUINT*O1SPDFFEJOHTPGUIFUI"$.
    4*(,%%*OUFSOBUJPOBM$POGFSFODFPO,OPXMFEHF%JTDPWFSZ%BUB.JOJOH QQr
    

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24. • ᶃ จ຺ͷ૿Ճʹ൐͏௥ैੑͷ௿Լ
    • ैདྷख๏Ͱ͸୯Ұͷจ຺Ͱൃੜ͢ΔใुͷมԽΛܭଌ
    • ཁҼͷύϥϝʔλ਺ʹରͯ͠ࢦ਺తʹ૿Ճ͢Δจ຺͝ͱʹใुΛ؍ଌ͢Δ৔
    ߹ɺཤྺͷ஝ੵ͕஗Εɺ௥ैੑʹ՝୊͕࢒Δ
    • ᶄ มԽݕग़ͱ௥ैʹඞཁͳཤྺσʔλͷαΠζංେԽ
    • มԽݕग़ͷͨΊͷࢦඪɺ௥ैͷͨΊͷࢼߦճ਺ͱใुͷཤྺ
    • → ཁҼͷύϥϝʔλ਺ʹൺྫͯ͠૿Ճ
    24
    ैདྷख๏Λઢܗ͔ͭඇఆৗ΁֦ு͢Δࡍͷ՝୊
    

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25. • ඇఆৗͳଟ࿹όϯσΟοτ໰୊ͷղ๏Λઢܗʹ֦ு
    • ैདྷख๏Λ൚༻తʹར༻Ͱ͖ɺׂҾܕΞϓϩʔνͱൺֱͯ͠΋ྑ͍ධՁ͕ಘ
    ΒΕ͍ͯΔɺมԽݕग़ܕΞϓϩʔνͰ͋ΔS-TS-ADWINͷ֦ு
    • ᶃͷରࡦ: จ຺͝ͱͷใुͰ͸ͳ͘ɺจ຺਺ʹΑΒͳ͍ࢦඪͱͯ͠ਪఆͨ͠
    ઢܗύϥϝʔλ͔ΒมԽݕग़͢Δ
    • ᶄͷରࡦ: ཁ໿σʔλߏ଄Λಋೖ͠ɺཤྺσʔλͷαΠζΛ௿ݮ͢Δ
    25
    ఏҊख๏
    

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26. จ຺਺ʹΑΒͳ͍ࢦඪΛ༻͍ͨ
    มԽݕग़
    

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27. • ࿹͝ͱʹෳ਺ͷจ຺͕͋Γɺจ຺ʹԠͯ͡ใु෼෍͕ܾ·Δଟ࿹όϯσΟοτ
    ໰୊ͷઃఆ
    • ຊݚڀใࠂͰ͸ɺจ຺͸ɺෳ਺ͷཁҼͷύϥϝʔλͷ૊Έ߹ΘͤͰදݱ͞
    Εͨঢ়ଶͷ͜ͱΛࢦ͢
    • → ཁҼύϥϝʔλͷ஋͕{0,1}ͷ৔߹ɺจ຺͸ཁҼ਺ ʹରͯ͠ ύλʔϯ
    d 2d
    27
    ઢܗͳଟ࿹όϯσΟοτ໰୊ʢ࠶ܝʣ
    • ઢܗͳଟ࿹όϯσΟοτ໰୊ͷղ๏Ͱ͸ɺจ຺ͷ֬཰෼෍Ͱ͸ͳ͘ɺཁҼ͝ͱ
    ͷ܎਺ʢઢܗύϥϝʔλʣΛਪఆ͢Δ͜ͱͰ֤จ຺ʹ͓͚ΔใुΛ༧૝͢Δ
    

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28. • ࢼߦ࣌ͷίϯςΩετ৘ใ ͱใु ͔Β࿹͝ͱͷઢܗύϥϝʔλΛਪఆ
    • ίϯςΩετ৘ใͷཁҼ਺ʢ=ઢܗύϥϝʔλͷཁҼ਺ʣ͸ ࣍ݩͱ͢Δ
    b r
    d
    28
    ઢܗύϥϝʔλͷਪఆ
    Bi = Bi + bbT
    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
    Bi =
    0
    B
    B
    B
    @
    b11 b12
    · · · b1d
    b21 b22
    · · · b2d
    .
    .
    .
    .
    .
    .
    .
    .
    .
    .
    .
    .
    bd1 bd2
    · · · bdd
    1
    C
    C
    C
    A
    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
    fi =
    0
    B
    B
    B
    @
    br1
    br2
    .
    .
    .
    brd
    1
    C
    C
    C
    A
    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
    fi = fi + br
    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
    ✓i =
    0
    B
    B
    B
    @
    ✓1
    ✓2
    .
    .
    .
    ✓d
    1
    C
    C
    C
    A
    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
    ✓i = B 1
    i
    fi
    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
    ର֯੒෼͸ͦͷཁҼͷࢼߦճ਺ɻ
    ͦͷଞͷ஋͸ɺର֯੒෼ͱͦͷཁҼͷ
    ૊Έ߹ΘͤʹΑΔࢼߦճ਺Λද͢ɻ
    ͦͷཁҼͷྦྷੵใुΛද͢ ͷٯߦྻͱ ͷੵΑΓཁҼ͝ͱͷઢ
    ܗύϥϝʔλΛਪఆ
    ʢཁҼ͕ഉଞͰ͋Ε͹ฏۉใुֹʣ
    B f
    

    View Slide

29. 29
    ઢܗύϥϝʔλͷࢦඪ
    • ࢦඪᶃ: ํ޲σʔλͷҟৗ౓
    • 1-(ઢܗύϥϝʔλͷฏۉͱͷ
    ίαΠϯྨࣅ౓)
    • ࢦඪᶄ: େ͖͞
    • ઢܗύϥϝʔλͷL2ϊϧϜ
    a = 1 (¯
    ✓T✓/(||¯
    ✓||2
    · ||✓||2))
    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
    m = ||✓||2
    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
    

    View Slide

30. • ਪఆͨ͠ઢܗύϥϝʔλͷ஋ͷҟৗ౓ͱେ͖͔͞ΒඇఆৗͳมԽΛݕग़͢Δ
    • → ཁҼ਺ʹΑΒͳ͍ݻఆ਺ͷ஋ͷΈ͔ΒมԽݕग़ʢ ʣ
    • ADWINʹΑͬͯมԽΛݕग़ͨ͠৔߹ɺมԽલͷࢼߦճ਺ɺྦྷੵใुΛআڈ
    2d → d → 2
    30
    ઢܗύϥϝʔλͷมԽݕग़ʢADWIN-Vʣ
    ✓i = B 1
    i
    fi
    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
    ᶄઢܗύϥϝʔλͷࢦඪ ᶅ࣌ܥྻͱͯ͠஋Λอଘ
    ᶆ"%8*/ʹΑΔ஋ ͷมԽݕग़
    m, a
    ᶇมԽલͷ஋Λআڈ
    ᶃઢܗύϥϝʔλͷਪఆ
    a = 1 (¯
    ✓T✓/(||¯
    ✓||2
    · ||✓||2))
    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
    m = ||✓||2
    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
    Am = {mt 100, mt 99, · · · , mt 1}
    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
    Aa = {at 100, at 99, · · · , at 1}
    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
    

    View Slide

31. ཁ໿σʔλߏ଄ʹΑΔ
    ཤྺσʔλαΠζͷ௿ݮ
    

    View Slide

32. • ᶃมԽݕग़ʹ༻͍Δཤྺσʔλʢཤྺظؒ x ࿹ͷ਺ʣ
    32
    ఏҊख๏ʹ͓͚Δཤྺσʔλ
    Am = {mt 100, mt 99, · · · , mt 1}
    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
    Aa = {at 100, at 99, · · · , at 1}
    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
    Bi =
    0
    B
    B
    B
    @
    b11 b12
    · · · b1d
    b21 b22
    · · · b2d
    .
    .
    .
    .
    .
    .
    .
    .
    .
    .
    .
    .
    bd1 bd2
    · · · bdd
    1
    C
    C
    C
    A
    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
    fi =
    0
    B
    B
    B
    @
    br1
    br2
    .
    .
    .
    brd
    1
    C
    C
    C
    A
    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
    a = 1 (¯
    ✓T✓/(||¯
    ✓||2
    · ||✓||2))
    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
    m = ||✓||2
    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
    E(f) = {ft 100, ft 99, · · · , ft 1}
    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
    E(B) = {Bt 100, Bt 99, · · · , Bt 1}
    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
    • ᶄมԽ௥ैʹ༻͍Δཤྺσʔλʢཤྺظؒ x ࿹ͷ਺ x ࣍ݩ਺ʣ
    

    View Slide

33. 33
    ࢦ਺ώετάϥϜ
    ද
    
    
    • ཤྺظؒʹର͢ΔσʔλͷαΠζΛ௿ݮ͢ΔͨΊࢦ਺ώετάϥϜ[3]Λಋೖ
    • ࣌ܥྻσʔλʹରͯ͠ɺ͋ΔظؒͷσʔλΛ߹ࢉͯ࣋ͭ͠ʢόέοτʣ
    • ߹ࢉ͢ΔظؒΛࢦ਺తʹେ͖͘͢Δ͜ͱͰཤྺظؒʹର͢Δσʔλߏ଄ͷ
    αΠζΛখ͘͞อͭ
    • όέοτ͸߹ࢉظؒͱ߹ࢉ஋ͷೋͭͷ஋Ͱදݱ͞ΕΔ
    <>l.BJOUBJOJOH4USFBN4UBUJTUJDTPWFS4MJEJOH8JOEPXTz .%BUBS "(JPOJT 1*OEZL 3.PUXBOJ"$.4*".
    Capacity
    Content
    …
    

    View Slide

34. • ᶃมԽݕग़ʹ༻͍Δཤྺσʔλʢཤྺظؒ x ࿹ͷ਺ʣ
    34
    มԽݕग़ͷཤྺσʔλαΠζͷ௿ݮ
    Am = {mt 100, mt 99, · · · , mt 1}
    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
    Aa = {at 100, at 99, · · · , at 1}
    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
    a = 1 (¯
    ✓T✓/(||¯
    ✓||2
    · ||✓||2))
    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
    m = ||✓||2
    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
    L2-Norm
    Anomaly
    score
    ADWIN2-V
    B−1f
    t t-1 t-2~3 t-4~5 t-6~9 t-10~13 t-14~20
    20 20 21 21 22 22 23
    20 20 21 21 22 22 23
    Capacity
    Content
    Capacity
    Content
    ADWIN2[2]
    Proposal
    

    View Slide

35. 35
    มԽ௥ैͷཤྺσʔλαΠζͷ௿ݮ
    Bi =
    0
    B
    B
    B
    @
    b11 b12
    · · · b1d
    b21 b22
    · · · b2d
    .
    .
    .
    .
    .
    .
    .
    .
    .
    .
    .
    .
    bd1 bd2
    · · · bdd
    1
    C
    C
    C
    A
    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
    fi =
    0
    B
    B
    B
    @
    br1
    br2
    .
    .
    .
    brd
    1
    C
    C
    C
    A
    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
    E(f) = {ft 100, ft 99, · · · , ft 1}
    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
    E(B) = {Bt 100, Bt 99, · · · , Bt 1}
    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
    • ᶄมԽ௥ैʹ༻͍Δཤྺσʔλʢཤྺظؒ x ࿹ͷ਺ x ࣍ݩ਺ʣ
    • ࢦ਺ώετάϥϜ͸1࣍ݩͷ࣌ܥྻσʔλΛର৅ͱ͍ͯ͠Δ
    • 1࣍ݩ͋ͨΓ2ͭͷσʔλ͕ඞཁ
    

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36. 36
    มԽ௥ैͷཤྺσʔλαΠζͷ௿ݮʢExpHist-Vʣ
    ϕΫτϧ୯Ґͷόέοτʹ֦ு͢Δ͜ͱͰෆཁͳϝλσʔλ΋࡟ݮ ( )
    2d′ → d′ + 1
    t t-1 t-2~3 t-4~5 t-6~9 t-10~13 t-14~20
    Extract
    ExpHist-V
    B
    ExpHist-V
    f Content
    Capacity
    Capacity 20 20 21 21 22 22 23
    Content
    20 20 21 21 22 22 23
    

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37. ैདྷͷઢܗͳղ๏΁ͷద༻
    

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38. • ઢܗͳଟ࿹όϯσΟοτ໰୊ͷղ๏Ͱ
    ͋ΔLinear Thompson Samplingͱ
    LinUCBʹద༻ʢݮਰૢ࡞ʹ΋ରԠʣ
    • มԽݕग़ʹΑΔ௥ैੑͱཤྺσʔλα
    Πζͷ௿ݮΛ࣮ݱ
    38
    ैདྷͷઢܗͳղ๏΁ͷద༻ʢAdaptive-Linear-MABʣ
    ਪఆͨ͠ઢܗύϥϝʔλʹΑΔมԽݕग़
    ཁ໿σʔλߏ଄ʹΑΔཤྺσʔλαΠζͷ௿ݮ
    

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39. 4.
    ධՁ
    

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40. • ඇఆৗͰઢܗͳଟ࿹όϯσΟοτ໰୊ʹର͢ΔੑೳΛධՁ͢ΔγϛϡϨʔγϣ
    ϯΛߦ͏ɻ
    • มԽ΁ͷ௥ैੑ͕޲্͢Δ͜ͱΛ֬ೝ
    • ཤྺσʔλαΠζ͕௿ݮ͢Δ͜ͱΛ֬ೝ
    40
    ධՁ
    

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41. • ઢܗͳ؀ڥͱͯ͠ɺཁҼ਺8͔ΒͳΔ256௨Γͷจ຺ʢ͝ͱͷใु෼෍ʣΛ࣋
    ͭ࿹0ͱ࿹1Λ༻ҙ͠ɺ2000࣌఺ܦաޙͷྦྷੵใुͳΒͼʹྦྷੵϦάϨοτΛ
    ֤ղ๏Ͱൺֱɻ
    • ඇఆৗͳ؀ڥͱͯ͠ɺ࿹1ͷΈ500࣌఺Ͱใु෼෍ΛมԽͤ͞Δɻ
    • ൺֱ͢Δղ๏͸ɺLinear Thompson SamplingɺLinUCBͷΞϧΰϦζϜʹର͠
    ͯݮਰʢDecay xxʣ΋͘͠͸ఏҊख๏Λద༻ͨ͠΋ͷʢAdaptive xxʣΛ༻͍
    Δɻ
    41
    γϛϡϨʔγϣϯઃఆ
    

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42. • طଘख๏Ͱ͸աڈͷ؍ଌ݁Ռ͕ѱ
    ӨڹΛٴ΅͠ྦྷੵϦάϨοτͷ૿
    Ճ͕ܧଓͨ͠
    • طଘͷݮਰख๏Ͱ͸աڈͷ؍ଌ݁
    ՌͷݮਰͷޮՌ͕ग़Δ·ͰྦྷੵϦ
    άϨοτͷ૿Ճ͕ݟΒΕͨ
    • ఏҊख๏ʢ࣮ઢʣͷద༻ʹΑΓม
    Խݕग़͕༗ޮʹಇ͖ɺྦྷੵϦά
    Ϩοτͷऩଋ·Ͱͷظ͕ؒ୹ॖ
    42
    ࢼߦճ਺ͱྦྷੵϦάϨοτ
    

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43. • ํ޲σʔλͷҟৗ౓ʢ্ஈʣͱେ͖
    ͞ʢԼஈʣʹؔͯ͠ɺैདྷख๏ʢ೾
    ઢʣͰ͸ɺਪఆ஋͕؇΍͔ʹਅͷ஋
    ʹ͖ۙͮɺఏҊख๏ʢ࣮ઢʣͰ͸ٸ
    ܹʹऩଋ
    • ఏҊख๏ͷADWIN-VʹΑͬͯ௚ۙͷ
    ؍ଌ݁ՌͷΈΛར༻Ͱ͖ͨͨΊ
    43
    ઢܗύϥϝʔλͷਪఆʢมԽ΁ͷ௥ैੑʣ
    

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44. • ʢ্ஈʣఏҊख๏ͷཤྺظؒͷਪҠɻ
    ઢܗύϥϝʔλͷਪఆʹͲͷఔ౓௚ۙ
    ·Ͱͷ؍ଌ݁ՌΛར༻͔ͨ͠Λࣔ͢
    • มԽ௚ޙʹཤྺΛগͳ͘ɺมԽ͕ͳ͍
    ৔߹͸ཤྺΛ௕͘อ࣋ͯ͠ਫ਼౓ͷ޲্
    Λਤ͍ͬͯΔ͜ͱ͕Θ͔Δ
    44
    ཤྺσʔλͷαΠζʢཁ໿σʔλߏ଄ʹΑΔ௿ݮʣ
    

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45. • ʢԼஈʣཁ໿σʔλߏ଄ʹΑΔཤྺ
    σʔλαΠζͷมԽ
    • ࣮ࡍͷཤྺظؒʹରͯ͠ඞཁͳσʔλ
    ͷαΠζͷංେԽΛ཈ࢭͰ͖ͨ
    • ҰํͰɺཤྺظ͕ؒ୹͍৔߹ʹ͸͕ࠩ
    ݟΒΕͳ͍৔߹΋֬ೝͨ͠ɻཤྺظؒ
    ͷࣄલܭଌʹΑΔಋೖݕ౼͸ඞཁɻ
    45
    ཤྺσʔλͷαΠζʢཁ໿σʔλߏ଄ʹΑΔ௿ݮʣ
    

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46. 5.
    ·ͱΊ
    

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47. • ਪનγεςϜΛ͸͡Ίͱ͢Δɺଟ༷͔ͭܧଓతʹมԽ͢Δ؀ڥΛ૝ఆͨ͠ଟ࿹
    όϯσΟοτ໰୊ͷղ๏ΛఏҊͨ͠
    • ैདྷͷઢܗɺඇఆৗͳղ๏Λ୯७ʹ૊Έ߹Θͤͨࡍʹൃੜ͢ΔҎԼͷ՝୊Λղ
    ܾ͢Δ൚༻తͳ֦ுͱͯ͠ఏҊ
    • จ຺ͷ૿Ճʹ൐͏௥ैੑͷ௿Լ → ਪఆͨ͠ઢܗύϥϝʔλ͔ΒมԽΛݕग़
    • มԽݕग़ͱ௥ैʹඞཁͳཤྺσʔλαΠζͷංେԽ → ཁ໿σʔλߏ଄
    • ධՁͰ͸ɺඇఆৗ͔ͭઢܗͳ؀ڥʹ͓͍ͯैདྷͷղ๏ʹରͯ͠ྦྷੵใुɺྦྷੵ
    ϦάϨοτʹ͓͍ͯੑೳͷ޲্ɺཤྺσʔλαΠζͷ௿ݮΛ֬ೝͨ͠ɻ
    47
    ·ͱΊ
    

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48. View Slide