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๏

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

1. ͸͡Ίʹ

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

• 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՝୊

• ͋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

• ͋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

2. ؔ࿈ݚڀ

• 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

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

• ࿹͝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

• ࿹͝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

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

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

• 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

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

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

• ࿹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

• ࿹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 ◆ AAADF3ichVE9b9RAEB2br8QEckCDFCk6cUo4ipzWASmIKhJNyuSSy4fi6LT2zV1W2Vtb672LDst/gJIGoVRBooj4AZQpkFBaCor8BEQZJCgoGPsMgUSEsex983be7FuPH0kRG8aOLfvS5StXr42MOtfHbtwcL926vRqHPR1gIwhlqNd9HqMUChtGGInrkUbe9SWu+TtPs/21PupYhGrFDCLc6vKOEm0RcENUs/TCk9g2VcfzsSNUwrXmgzSRFKmzogWXzcSk5enyLzzjZpkXtEIT/0mr1POcOu5y3SoUv5MzklNepY6HqlUc6nhadLbNA6dZqrAay6N8HrgFqEARi2HpHXjQghAC6EEXEBQYwhI4xPRsggsMIuK2ICFOExL5PkIKDml7VIVUwYndoW+Hss2CVZRnPeNcHdApkl5NyjJMsU/sgJ2wI/aWfWY//tkryXtkXga0+kMtRs3x53eXv/1X1aXVwPap6kLPBtrwOPcqyHuUM9ktgqG+/+zlyfKT+lQyzV6zL+R/nx2z93QD1f8avFnC+t4FfnzyQn+MBuSeHcd5sDpbcx/WZpceVeY3ilGNwATcgyrNYw7mYQEWoUH9v1uT1n2rar+yD+0P9tGw1LYKzR34K+yPPwFXgsYt มԽલ มԽޙ

3. ఏҊख๏

• 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

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՝୊

• 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

• 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՝୊

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

จ຺਺ʹΑΒͳ͍ࢦඪΛ༻͍ͨ มԽݕग़

• ࿹͝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

• ࢼߦ࣌ͷίϯςΩετ৘ใ ͱใु ͔Β࿹͝ͱͷઢܗύϥϝʔλΛਪఆ • ίϯςΩετ৘ใͷཁҼ਺ʢ=ઢܗύϥϝʔλͷཁҼ਺ʣ͸ ࣍ݩͱ͢Δ b r d 28 ઢܗύϥϝʔλͷਪఆ Bi = Bi + bbT AAACpnichVFNLwNBGH66vqq+iovEBQ2RSJopEiKRCBcn0VIlSu2uKZPuV3anTdj0LPEHHJxIHERc+QEu/oCDnyCOJC4O3m43EQTvZmaeeeZ93n1mXs0xhCcZe4woDY1NzS3R1lhbe0dnV7y7Z82zy67Os7pt2O66pnrcEBbPSiENvu64XDU1g+e00kLtPFfhridsa1UeOHzLVPcsURS6KokqxAfnC2KWxlheM32tWp+3/bypyn2v6K9Wq4V4giVZEAM/QSoECYSxbMdvkccubOgowwSHBUnYgAqPvk2kwOAQtwWfOJeQCM45qoiRtkxZnDJUYks079FuM2Qt2tdqeoFap78YNFxSDmCYPbBL9sLu2RV7Yu+/1vKDGjUvB7RqdS13Cl3HfStv/6pMWiX2P1V/epYoYjrwKsi7EzC1W+h1feXw5GVlJjPsj7Bz9kz+z9gju6MbWJVX/SLNM6d/+NHIC70YNSj1vR0/wdp4MjWRHE9PJuY2wlZF0Y8hjFI/pjCHRSwjS/WPcI0b3CqjypKSVXL1VCUSanrxJZSdD5HLngo= 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

29 ઢܗύϥϝʔλͷࢦඪ • ࢦඪᶃ: ํ޲σʔλͷҟৗ౓ • 1-(ઢܗύϥϝʔλͷฏۉͱͷ ίαΠϯྨࣅ౓) • ࢦඪᶄ: େ͖͞ • ઢܗύϥϝʔλͷL2ϊϧϜ a = 1 (¯ ✓T✓/(||¯ ✓||2 · ||✓||2)) AAAC5nichVE9T9tQFD1xoQUKTVoWpC5WI6owEJ7TSq0qISFYOgJJAAnT6Nm8EAt/yX6JRJ38AQY2lIEFKnWo+gP4AQz0D3TgJ1RVJypYGHrtWG0hAq5lv/POvef6vHcN37ZCydhZRnkwMPjw0dDwyOPRsSfZ3NNnK6HXDExRNT3bC9YMHgrbckVVWtIWa34guGPYYtXYXojzqy0RhJbnVuSOLzYcvuVadcvkkqhajnN1VtWmC7rBg0g3nEiXDSF5p/NBd7hshPWo0vmPnim0232l7XatpOrmpifVOPs3EfNTU7VcnhVZEmo/0FKQRxqLXu4YOjbhwUQTDgRcSMI2OEJ61qGBwSduAxFxASEryQt0MELaJlUJquDEbtN3i3brKevSPu4ZJmqT/mLTG5BSxST7zr6wc/aNfWU/2NWtvaKkR+xlh1ajpxV+Lbs7Ub68V+XQKtH4p7rTs0QdbxOvFnn3EyY+hdnTtz52z8vvliejl+wT+0n+j9gZO6ETuK3f5uclsXxwhx+DvNCN0YC0m+PoByulovaqWFp6nZ+bT0c1hOd4gQLN4w3m8B6LqFL/U/zCBS6VhrKn7CvdXqmSSTXjuBbK4R+0/riw m = ||✓||2 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

• 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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

ཁ໿σʔλߏ଄ʹΑΔ ཤྺσʔλαΠζͷ௿ݮ

• 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

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 …

• 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} AAACtXichVHLTttQED0YSnkU4tJNJTZRIyoWIRrTSjykSrRsWAIhgIRDZDs3wcIv2TeRqOUf6Ae0C1at1AXiA9iwq4r4gS7yCYgllbphwcSxVNGoMJZ9z5w7Z3zuHTNw7EgSdQaUwaEnw09HRsfGn01M5tTnU9uR3wotUbF8xw93TSMSju2JirSlI3aDUBiu6Ygd83C1u7/TFmFk+96WPApE1TWant2wLUMyVVNJN934fVIz8u/yemzsx3JOI0qKKVpaSoq6Vfdl1Mu1RE9qaoFKlEa+H2gZKCCLdV89g446fFhowYWAB8nYgYGInz1oIATMVREzFzKy032BBGOsbXGV4AqD2UP+Njnby1iP827PKFVb/BeH35CVeczQLzqhG7qkU7qi2//2itMeXS9HvJo9rQhquU8vy38eVbm8Shz8VT3oWaKBxdSrzd6DlOmewurp2x+/3JSXN2fi1/SNrtn/V+rQDz6B1/5tfd8Qm8cP+DHZC98YD0j7dxz9YHu+pL0pzW+8Lax8yEY1gmm8wizPYwErWMM6Ktz/M87xExfKglJV6kqjV6oMZJoXuBeKfwf2TqIM 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

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

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

ैདྷͷઢܗͳղ๏΁ͷద༻

• 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

4. ධՁ

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

• 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

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

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

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

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

5. ·ͱΊ

• 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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