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仮想的な探索を用いて文脈や時間の経過による番狂わせにも迅速に追従する多腕バンディット手法/wi...

monochromegane
December 17, 2021

 仮想的な探索を用いて文脈や時間の経過による番狂わせにも迅速に追従する多腕バンディット手法/wi2_lkf_bandits

2021.12.17 ARG 第17回Webインテリジェンスとインタラクション研究会
https://www.sigwi2.org/cfano17

monochromegane

December 17, 2021
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  1. ࡾ୐ ༔հ1,2ɺ็ ߃ݑ3 1. Pepabo R&D Institute, GMO Pepabo, Inc.,

    2. ۝भେֶ େֶӃγεςϜ৘ใՊֶ෎ ৘ใ஌ೳ޻ֶઐ߈ 3. ۝भେֶ େֶӃγεςϜ৘ใՊֶݚڀӃ ৘ใ஌ೳ޻ֶ෦໳ 2021.12.17 ARG ୈ17ճWebΠϯςϦδΣϯεͱΠϯλϥΫγϣϯݚڀձ Ծ૝తͳ୳ࡧΛ༻͍ͯ จ຺΍࣌ؒͷܦաʹΑΔ൪ڰΘͤʹ΋ ਝ଎ʹ௥ै͢Δଟ࿹όϯσΟοτख๏
  2. • దԠతͳγεςϜͷ࣮ݱʹ͸ɺγεςϜ͕ར༻ऀͷঢ়گΛΑ͘஌Δ͜ͱ͕ॏཁ • ECαΠτͷγεςϜͰ͋Ε͹ɺར༻ऀͷᅂ޷Λ೺Ѳ͢Δ͜ͱͰɺ࠷దͳ঎ ඼ΛఏҊͰ͖Δ • ࣮ӡ༻ͷγεςϜʹ͓͍ͯίϛϡχέʔγϣϯʹ͸ίετ͕͔͔Δ • ʢར༻ऀࣗ਎΋ؚΊͯʣཁٻ΍ᅂ޷͸໌֬Ͱ͸ͳ͘ঃʑʹܗ੒͞Ε͍ͯ͘ •

    ͦͷظؒதͷෛ୲΍ػձଛࣦ͸୹ظ௕ظͰചΓ্͛ͳͲʹӨڹ͢Δ • ಛʹɺཁٻ΍ᅂ޷͕มԽ͢Δ؀ڥͰ͸ɺݱ࣌఺ͰՁ஋ͷ௿͍ίϛϡχέʔ γϣϯ΋ܧଓͯ͠ߦ͏ඞཁ͕͋Δ 4 దԠతͳγεςϜͱίϛϡχέʔγϣϯίετ
  3. • ࿹ͷ༗༻ੑ͸ɺจ຺΍࣌ؒͷܦաʹԠͯ͡มԽ͢Δ[*] • ଟ࿹όϯσΟοτͷํࡦ͸ɺ͋Δ࣌఺ͰධՁͷߴ͍࿹Λ࠷΋ଟ͘׆༻͢Δ • ࿹ͷ༗༻ੑͷมԽͷ൑அʹ͸ɺมԽޙͷใु෼෍͔Βͷαϯϓϧ͕Ұఆ਺ඞཁ 16 ଟ࿹όϯσΟοτ໰୊ʹ͓͚Δ൪ڰΘͤͷ՝୊ ൪ڰΘͤͳ੾ΓସΘΓ •

    ൪ڰΘͤͷݕग़ͷͨΊʹશͯͷ࿹΁ͷ୳ࡧΛ Ұ཯ʹ૿΍͢[1]ͱมԽ͕ͳ͍ظؒ΍จ຺Ͱͷ ػձଛࣦʹͭͳ͕Δ <>$BP : 8FO ; ,WFUPO # 9JF :  /FBSMZ0QUJNBM"EBQUJWF1SPDFEVSFXJUI$IBOHF%FUFDUJPOGPS1JFDFXJTF4UBUJPOBSZ#BOEJU1SPDFFEJOHTPG.BDIJOF-FBSOJOH3FTFBSDI  r 1.-3
  4. 18 ैདྷͷଟ࿹όϯσΟοτํࡦͱ൪ڰΘͤ΁ͷରԠ จ຺ ਝ଎ͳධՁߋ৽ ޮ཰తͳ୳ࡧ ࣮ߦ࣌ؒ %FDBZ-JO6$#<> P P Y

    P "E54<> P P Y Y E-JO6$#<> P P ˚ P %FO#BOE<> P P ˚ P 5751<> P P Y Y "%"*-5$# <> P P ˚ Y ,'."/#<> Y P P P
  5. 19 ैདྷͷଟ࿹όϯσΟοτํࡦͱ൪ڰΘͤ΁ͷରԠ จ຺ ਝ଎ͳධՁߋ৽ ޮ཰తͳ୳ࡧ ࣮ߦ࣌ؒ %FDBZ-JO6$#<> P P Y

    P "E54<> P P Y Y E-JO6$#<> P P ˚ P %FO#BOE<> P P ˚ ˚ 5751<> P P Y Y "%"*-5$# <> P P ˚ Y ,'."/#<> Y P P P <>$IVORJV;FOH 2JOH8BOH 4IFLPPGFI.PLIUBSJ BOE5BP-J0OMJOFDPOUFYUBXBSFSFDPNNFOEBUJPOXJUIUJNFWBSZJOHNVMUJBSNFECBOEJU*O1SPDFFEJOHTPGUIFOE"$.4*(,%%JOUFSOBUJPOBM DPOGFSFODFPO,OPXMFEHFEJTDPWFSZBOEEBUBNJOJOH QQr  <>/FHBS)BSJSJ #BNTIBE.PCBTIFS BOE3PCJO#VSLF"EBQUJOHUPVTFSQSFGFSFODFDIBOHFTJOJOUFSBDUJWFSFDPNNFOEBUJPO*O5XFOUZ'PVSUI*OUFSOBUJPOBM+PJOU$POGFSFODFPO"SUJpDJBM*OUFMMJHFODF   <>.VIBNNBE"NNBS)BTTBO/PO4UBUJPOBSZ$POUFYUVBM.VMUJ"SNFE#BOEJUXJUI"QQMJDBUJPOJO0OMJOF3FDPNNFOEBUJPOT1I%UIFTJT 6OJWFSTJUZPG7JSHJOJB  <>2JOHZVO8V /BWFFO*ZFS BOE)POHOJOH8BOH-FBSOJOHDPOUFYUVBMCBOEJUTJOBOPOTUBUJPOBSZFOWJSPONFOU*O5IFTU*OUFSOBUJPOBM"$.4*(*3$POGFSFODFPO3FTFBSDI%FWFMPQNFOUJO *OGPSNBUJPO3FUSJFWBM QQr  <>2JOHZVO8V )VB[IFOH8BOH :BOFO-J BOE)POHOJOH8BOH%ZOBNJDFOTFNCMFPGDPOUFYUVBMCBOEJUTUPTBUJTGZVTFST`DIBOHJOHJOUFSFTUT*O5IF8PSME8JEF8FC$POGFSFODF QQr  <>:JGBOH$IFO $IVOH8FJ-FF )BJQFOH-VP BOE$IFO:V8FJ"OFXBMHPSJUINGPSOPOTUBUJPOBSZDPOUFYUVBMCBOEJUT&⒏DJFOU PQUJNBMBOEQBSBNFUFSGSFF*O$POGFSFODFPO-FBSOJOH5IFPSZ QQ r1.-3  <>0MF$ISJTUP⒎FS(SBONPBOE4UJBO#FSH4PMWJOHOPOTUBUJPOBSZCBOEJUQSPCMFNTCZSBOEPNTBNQMJOHGSPNTJCMJOHLBMNBOpMUFST*O*OUFSOBUJPOBM$POGFSFODFPO*OEVTUSJBM &OHJOFFSJOHBOE0UIFS "QQMJDBUJPOTPG"QQMJFE*OUFMMJHFOU4ZTUFNT QQr4QSJOHFS 
  6. • ͜ͷ໰୊Λਝ଎͔ͭޮ཰తʹղܾ͢Δํࡦ͸ҎԼͷཁ݅Λຬͨ͢ • จ຺Λѻ͏͜ͱ͕Ͱ͖Δ • ࿹ͷਝ଎ͳධՁߋ৽ͷ࢓૊ΈΛඋ͑Δ • ධՁͷ௿͍࿹΁ͷޮ཰తͳ୳ࡧͷ࢓૊ΈΛඋ͑Δ • ͜ΕΒͷ࢓૊Έͷ࣮ߦ͕࣌ؒগͳ͍

    • → KF-MANBΛআ͘ैདྷͷํࡦ͸ɺબఆͨ͠࿹ͷධՁͷΈΛ༻͍࣮ͯݱ͢Δ • → બఆ͠ͳ͔ͬͨ࿹ͷධՁ΋ಉ࣌ʹߋ৽Ͱ͖Ε͹ɺΑΓޮՌతͰ͸ͳ͍͔ ɹ ఏҊख๏Ͱ͸͜ͷͨΊʹʮઢܗΧϧϚϯϑΟϧλʯΛ࠾༻͢Δ 22 จ຺ͱɺ൪ڰΘͤΛؚΉඇఆৗੑ΁ͷରॲ
  7. 23 ैདྷͷଟ࿹όϯσΟοτํࡦͱ൪ڰΘͤ΁ͷରԠ จ຺ ਝ଎ͳධՁߋ৽ ޮ཰తͳ୳ࡧ ࣮ߦ࣌ؒ %FDBZ-JO6$#<> P P Y

    P "E54<> P P Y Y E-JO6$#<> P P ˚ P %FO#BOE<> P P ˚ P 5751<> P P Y Y "%"*-5$# <> P P ˚ Y ,'."/#<> Y P P P ఏҊख๏ P P P P
  8. 24 ํࣜͷྨࣅ͢Δख๏ͱͷࠩҟ จ຺ ਝ଎ͳධՁߋ৽ ޮ཰తͳ୳ࡧ ࣮ߦ࣌ؒ ,'."/#<> Y P P

    P ఏҊख๏ P P P P • ਝ଎ͳධՁߋ৽ͱऑ͍࿹΁ͷޮ཰తͳ୳ࡧͷͨΊɺܰྔͳΧϧϚϯϑΟϧλΛར༻͢Δ఺ ͕ڞ௨ • ఏҊख๏͸ઢܗΧϧϚϯϑΟϧλΛར༻͢Δ఺͕ҟͳΔ • ࣌ؒͷܦա͚ͩͰͳ͘จ຺ʹΑͬͯ΋࿹ͷ༗ޮੑ͕ҟͳΔ؀ڥʹద༻Ͱ͖Δ • τϨϯυ΍पظత੒෼Λߟྀͨ͠ɺΑΓޮ཰తͳ୳ࡧ͕ظ଴Ͱ͖Δ <>0MF$ISJTUP⒎FS(SBONPBOE4UJBO#FSH4PMWJOHOPOTUBUJPOBSZCBOEJUQSPCMFNTCZSBOEPNTBNQMJOHGSPNTJCMJOHLBMNBOpMUFST*O*OUFSOBUJPOBM$POGFSFODFPO*OEVTUSJBM &OHJOFFSJOHBOE0UIFS "QQMJDBUJPOTPG"QQMJFE*OUFMMJHFOU4ZTUFNT QQr4QSJOHFS 
  9. • Ұظઌ༧ଌͱ؍ଌ݁ՌʹΑΔϑΟϧλϦϯάΛ܁Γฦͯ͠ঢ়ଶΛܧଓతʹਪఆ • ঢ়ଶ ͸ฏۉ ͱͦͷ෼ࢄڞ෼ࢄ Ͱදݱ͢Δ͜ͱ͕Ͱ͖Δ α μ P

    27 1. ઢܗΧϧϚϯϑΟϧλʹΑΔ࿹ͷঢ়ଶਪఆ Ұظઌͷঢ়ଶ༧ଌ Ұظઌͷ؍ଌ༧ଌ ؍ଌͷޡࠩ ϑΟϧλϦϯά ઢܗΧϧϚϯϑΟϧλʹ͓͚Δঢ়ଶߋ৽ͷαΠΫϧ t = t + 1 <latexit sha1_base64="VUdnMLAFVZPBHlSiKxWJLDz2ElQ=">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</latexit> µt+1 = Tµt|t Pt+1 = TPt|t TT + RQRT <latexit sha1_base64="HRYMQ8d6BFhrV94UjkWxn/4MPOI=">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</latexit> µt|t = µt + Kvt = µt + (PtZTF 1 t )vt Pt|t = Pt KFtKT <latexit sha1_base64="c9JcpZwYoLYc2KvKMX5kFsilLbI=">AAADBHichVFLS+NQFD6Jr1pf9TEguAkWizJYbqowgyDICCJ0U61V0WhIMrcamhfJbaHG4M7F/IFZuFJwIc5uGGY3m9n4B1z0B7gYZqngxoUnacAX6gnJPfc75/vy3XtUx9A9RkiD41ta29o7Ep3Jru6e3r5U/8CqZ1ddjZY027DddVXxqKFbtMR0ZtB1x6WKqRp0Ta3Mh/W1GnU93bZWWN2hW6ayY+llXVMYQnLqQFJNXzKrss/2WRAImVkhRgKZCR+FfLirYS5Jyczsk9J4QWYb25KpsF2v7K8ECzLb9ifFYOIRpdDUDWWxW5gU8tiVf0SSU2mSJVEILxMxTtIQR8FO/QYJvoINGlTBBAoWMMwNUMDDZxNEIOAgtgU+Yi5melSnEEASuVXsotihIFrB7w7uNmPUwn2o6UVsDf9i4OsiU4AxcknOyDW5IOfkH7l7VcuPNEIvdVzVJpc6ct+34eLtuywTVwa7D6w3PTMow+fIq47enQgJT6E1+bW979fFmeUxP0NOyH/0f0wa5C+ewKrdaKdLdPnoDT8qesEbwwGJz8fxMlnNZcWpbG5pOj33JR5VAkZgFMZxHp9gDhahACXUv+K6uCHuA3/I/+B/8r+arTwXcwbhSfB/7gH5GL88</latexit> vt = yt ˆ yt Ft = ZPtZ T + H <latexit sha1_base64="5CGzvCsqCzyEmpk7BFtJ5+zd9FU=">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</latexit> ˆ yt = Zµt <latexit sha1_base64="sOqAisWQEAZIxvyNoh5E7NBLmlI=">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</latexit>
  10. • ઢܗΧϧϚϯϑΟϧλʹΑΓ࿹͝ͱͷঢ়ଶͷฏۉͱ෼ࢄڞ෼ࢄΛಘΔ • ಘΒΕͨঢ়ଶͷฏۉͱ෼ࢄڞ෼ࢄΛɺฏۉͱ෼ࢄڞ෼ࢄͱ͢Δଟมྔਖ਼ن෼෍ ͔ΒαϯϓϦϯάΛߦ͏ • → ઢܗΧϧϚϯϑΟϧλͷਪఆ஋Λ༻͍ͨ֬཰Ұக๏ 28 2.

    ঢ়ଶਪఆ஋Λ༻͍ͨ֬཰Ұக๏ʹΑΔ࿹ͷબఆ ଟ࿹όϯσΟοτ໰୊ͱͯ͠ͷ୳ࡧͷ όϥϯεΛௐ੔͢Δεέʔϧ߲ Λಋೖ β খɹɹঢ়ଶɹɹେ ֬཰ີ౓ ଟ͘ͷ৔߹ɺ྘͕બఆ͞Ε Δ͕ɺ੄໺ͷ޿͍ΦϨϯδ ΋બఆ͞ΕΔՄೳੑ͕͋Δ
  11. • Ұظઌ༧ଌͱ؍ଌ݁ՌʹΑΔϑΟϧλϦϯάΛ܁Γฦͯ͠ঢ়ଶΛܧଓతʹਪఆ • ঢ়ଶ ͸ฏۉ ͱͦͷ෼ࢄڞ෼ࢄ Ͱදݱ͢Δ͜ͱ͕Ͱ͖Δ α μ P

    30 ઢܗΧϧϚϯϑΟϧλʹΑΔ࿹ͷঢ়ଶਪఆʢ࠶ܝʣ Ұظઌͷঢ়ଶ༧ଌ Ұظઌͷ؍ଌ༧ଌ ؍ଌͷޡࠩ ϑΟϧλϦϯά ઢܗΧϧϚϯϑΟϧλʹ͓͚Δঢ়ଶߋ৽ͷαΠΫϧ t = t + 1 <latexit sha1_base64="VUdnMLAFVZPBHlSiKxWJLDz2ElQ=">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</latexit> µt+1 = Tµt|t Pt+1 = TPt|t TT + RQRT <latexit sha1_base64="HRYMQ8d6BFhrV94UjkWxn/4MPOI=">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</latexit> µt|t = µt + Kvt = µt + (PtZTF 1 t )vt Pt|t = Pt KFtKT <latexit sha1_base64="c9JcpZwYoLYc2KvKMX5kFsilLbI=">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</latexit> vt = yt ˆ yt Ft = ZPtZ T + H <latexit sha1_base64="5CGzvCsqCzyEmpk7BFtJ5+zd9FU=">AAACxHichVFNS+NQFD2No1PrV3U2gptiUQSZ8uoIiiCKgnTZqlXROCGJrzaYL5LXQg2dH+AfmMWsFLoQf8D8gNkMzHa68CeISwU3Lrz5gGEU9YbknXvePTfnvau5puELxq5TUs+H3r6P6f7MwODQ8Eh2dGzHdxqezqu6Yzrenqb63DRsXhWGMPme63HV0ky+q52sh/u7Te75hmNvi5bLDy312DZqhq4KopTsiqxZQbOtiNz0ci7ELcKf5boqgjijVJYzG3HBflkR+19lSxV1vxZst2dLSjbPCiyK3EtQTEAeSZSd7E/IOIIDHQ1Y4LAhCJtQ4dNzgCIYXOIOERDnETKifY42MqRtUBWnCpXYE/oeU3aQsDblYU8/Uuv0F5Nej5Q5TLEuu2R37De7Yjfs8dVeQdQj9NKiVYu13FVGzsa3Ht5VWbQK1P+p3vQsUMNi5NUg727EhKfQY33z9Pvd1tLmVDDNLtgt+T9n1+wXncBu3uudCt/88YYfjbzQjdGAis/H8RLszBWKXwpzlfn86loyqjQmMIkZmscCVlFCGVXq38Ef/EVX2pBMyZcacamUSjSf8F9I354ANqupFA==</latexit> ˆ yt = Zµt <latexit sha1_base64="sOqAisWQEAZIxvyNoh5E7NBLmlI=">AAACoXichVE9S8NQFD3Gr/pddRF0KBbFqbyqoAiC6KJbba2KrZQkvrah+SJ5LdTQxdE/4OCkIChOuvgDXPwDDv0J4qjg4uBNGhAV9YbknXvePTfnvavYuuYKxpptUntHZ1d3pKe3r39gcCg6PLLtWlVH5VnV0i1nV5FdrmsmzwpN6HzXdrhsKDrfUSpr/v5OjTuuZplbom7zfUMumVpRU2VBVCE6kS/LwssrhldvNAoithzb85O8UaWsEI2zBAsi9hMkQxBHGCkreoc8DmBBRRUGOEwIwjpkuPTkkASDTdw+POIcQlqwz9FAL2mrVMWpQia2Qt8SZbmQNSn3e7qBWqW/6PQ6pIxhij2yK/bCHtg1e2Lvv/bygh6+lzqtSkvL7cLQ8Vjm7V+VQatA+VP1p2eBIhYDrxp5twPGP4Xa0tcOT14yS+kpb5qds2fyf8aa7J5OYNZe1YtNnj79w49CXujGaEDJ7+P4CbZnE8m5xOzmfHxlNRxVBOOYxAzNYwErWEcKWep/hEvc4FaKSxtSSkq3SqW2UDOKLyHlPgBnm5vF</latexit>
  12. • Ұظઌ༧ଌͱ؍ଌ݁ՌʹΑΔϑΟϧλϦϯάΛ܁Γฦͯ͠ঢ়ଶΛܧଓతʹਪఆ • ঢ়ଶ ͸ฏۉ ͱͦͷ෼ࢄڞ෼ࢄ Ͱදݱ͢Δ͜ͱ͕Ͱ͖Δ α μ P

    31 ઢܗΧϧϚϯϑΟϧλʹΑΔ࿹ͷঢ়ଶਪఆ Ұظઌͷঢ়ଶ༧ଌ Ұظઌͷ؍ଌ༧ଌ ؍ଌͷޡࠩ ϑΟϧλϦϯά ઢܗΧϧϚϯϑΟϧλʹ͓͚Δঢ়ଶߋ৽ͷαΠΫϧ t = t + 1 <latexit sha1_base64="VUdnMLAFVZPBHlSiKxWJLDz2ElQ=">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</latexit> µt+1 = Tµt|t Pt+1 = TPt|t TT + RQRT <latexit sha1_base64="HRYMQ8d6BFhrV94UjkWxn/4MPOI=">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</latexit> µt|t = µt + Kvt = µt + (PtZTF 1 t )vt Pt|t = Pt KFtKT <latexit sha1_base64="c9JcpZwYoLYc2KvKMX5kFsilLbI=">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</latexit> vt = yt ˆ yt Ft = ZPtZ T + H <latexit sha1_base64="5CGzvCsqCzyEmpk7BFtJ5+zd9FU=">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</latexit> ˆ yt = Zµt <latexit sha1_base64="sOqAisWQEAZIxvyNoh5E7NBLmlI=">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</latexit> ෼ࢄڞ෼ࢄΛখ͘͞ ෼ࢄڞ෼ࢄΛେ͖͘
  13. • ઢܗΧϧϚϯϑΟϧλͰ͸؍ଌ஋͕ಘΒΕͳ͍৔߹΋ܽଛ஋ͱͯ͠ѻ͑Δ • ͜ͷܽଛ஋ॲཧΛબఆ͞Εͳ͔ͬͨ࿹ʹର͢Δߋ৽ૢ࡞ͱͯ͠औΓೖΕΔ 32 ܽଛ஋ॲཧʹΑΔ୳ࡧͷଅਐ Ұظઌͷঢ়ଶ༧ଌ ϑΟϧλϦϯά ઢܗΧϧϚϯϑΟϧλʹ͓͚Δܽଛ஋ॲཧͷαΠΫϧ t

    = t + 1 <latexit sha1_base64="VUdnMLAFVZPBHlSiKxWJLDz2ElQ=">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</latexit> µt+1 = Tµt|t Pt+1 = TPt|t TT + RQRT <latexit sha1_base64="HRYMQ8d6BFhrV94UjkWxn/4MPOI=">AAAC03ichVE9SyRBEH3O6amrnuuZCCbiogjC0uMdKIIgmhjJfroLji4zc706OF/M9C54c5OIkWBsYKRgIKaCP+CS+wMGmmoihiuYGFg7O9zpyXk19HTVq3rVr7s01zR8wdhVm/ShveNjZ1d3oqe371N/cuDziu/UPJ0Xdcd0vLKm+tw0bF4UhjB52fW4amkmL2lbi818qc4933Dsgth2+ZqlbthG1dBVQVAluaxoVqBYtbASiEk5HJ8rvAB+iFBREpnfqUwLK6wrlio2/WpQCCdz2dyLsJJMsTSLbOStI8dOCrFlnOQFFHyDAx01WOCwIcg3ocKnbxUyGFzC1hAQ5pFnRHmOEAni1qiKU4VK6Bb9NyhajVGb4mZPP2LrdIpJyyPmCMbYJTtlDfaLnbE79vTPXkHUo6llm3atxeVupX9vKP/4X5ZFu8DmH9a7mgWqmIm0GqTdjZDmLfQWv/79oJGfzY0F4+yY3ZP+I3bFftIN7PqDfpLlucN39GikhV6MBiT/PY63zspUWv6Snsp+Tc0vxKPqwjBGMUHzmMY8lpBBkfqf4xo3uJWKUiDtSLutUqkt5gzilUn7z7XisIo=</latexit> µt|t = µt Pt|t = Pt <latexit sha1_base64="CWgdnJ0SnbvwjFOhwwEfDMRK7p8=">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</latexit> ෼ࢄڞ෼ࢄΛେ͖͘
  14. • ઢܗΧϧϚϯϑΟϧλͰ͸؍ଌ஋͕ಘΒΕͳ͍৔߹΋ܽଛ஋ͱͯ͠ѻ͑Δ • ͜ͷܽଛ஋ॲཧΛબఆ͞Εͳ͔ͬͨ࿹ʹର͢Δߋ৽ૢ࡞ͱͯ͠औΓೖΕΔ 33 ܽଛ஋ॲཧʹΑΔ୳ࡧͷଅਐ Ұظઌͷঢ়ଶ༧ଌ ϑΟϧλϦϯά ઢܗΧϧϚϯϑΟϧλʹ͓͚Δܽଛ஋ॲཧͷαΠΫϧ t

    = t + 1 <latexit sha1_base64="VUdnMLAFVZPBHlSiKxWJLDz2ElQ=">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</latexit> µt+1 = Tµt|t Pt+1 = TPt|t TT + RQRT <latexit sha1_base64="HRYMQ8d6BFhrV94UjkWxn/4MPOI=">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</latexit> µt|t = µt Pt|t = Pt <latexit sha1_base64="CWgdnJ0SnbvwjFOhwwEfDMRK7p8=">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</latexit> ෼ࢄڞ෼ࢄΛେ͖͘ ظ଴͞ΕΔޮՌͦͷ ֬཰Ұக๏ͷ࢓૊ΈʹΑΓબఆػձͷগͳ͍࿹ʹର͢Δ୳ࡧ͕ଅਐ͞ΕΔ
  15. • ઢܗΧϧϚϯϑΟϧλͰ͸؍ଌ஋͕ಘΒΕͳ͍৔߹΋ܽଛ஋ͱͯ͠ѻ͑Δ • ͜ͷܽଛ஋ॲཧΛબఆ͞Εͳ͔ͬͨ࿹ʹର͢Δߋ৽ૢ࡞ͱͯ͠औΓೖΕΔ 34 ܽଛ஋ॲཧʹΑΔঢ়ଶ֬ೝͷলུ Ұظઌͷঢ়ଶ༧ଌ ϑΟϧλϦϯά ઢܗΧϧϚϯϑΟϧλʹ͓͚Δܽଛ஋ॲཧͷαΠΫϧ t

    = t + 1 <latexit sha1_base64="VUdnMLAFVZPBHlSiKxWJLDz2ElQ=">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</latexit> µt+1 = Tµt|t Pt+1 = TPt|t TT + RQRT <latexit sha1_base64="HRYMQ8d6BFhrV94UjkWxn/4MPOI=">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</latexit> µt|t = µt Pt|t = Pt <latexit sha1_base64="CWgdnJ0SnbvwjFOhwwEfDMRK7p8=">AAACsnichVFLL8RQFP7UezxmsJHYTEyIjckdJEQiETaW4zEIlUlb12imr7R3JqH6B2wtLKxILMQPEFs2/oDF/ASxJLGxcNqpeAWnae93vnu+0+/eozqG7gnGag1SY1NzS2tbe6Kjs6s7merpXfXsiqvxgmYbtruuKh43dIsXhC4Mvu64XDFVg6+p5flwf63KXU+3rRWx5/AtUylZ+o6uKYKoYmpUVk1fNitB0RcHIhie+ZQHspzIv/MhCIqpDMuyKNI/QS4GGcSRt1NXkLENGxoqMMFhQRA2oMCjZxM5MDjEbcEnziWkR/scARKkrVAVpwqF2DJ9S5RtxqxFedjTi9Qa/cWg1yVlGkPsnl2wJ3bHLtkDe/21lx/1CL3s0arWtdwpJg/7l1/+VZm0Cux+qP70LLCDqcirTt6diAlPodX11f3jp+XppSF/mJ2xR/J/ymrslk5gVZ+180W+dPKHH5W80I3RgHLfx/ETrI5lc+PZscWJzOxcPKo2DGAQIzSPScxiAXkUqP8RrnGDW2lC2pAUSauXSg2xpg9fQjLeAJwJo1o=</latexit> τϨϯυ΍पظత੒෼Λߟྀͨ͠༧ଌ ظ଴͞ΕΔޮՌͦͷ ঢ়ଶͷਪҠ܏޲ͷ༧ଌʹΑΓɺ੾ସ·ͰͷܦաΛ೺Ѳ͢ΔͨΊͷ୳ࡧΛল͚Δ
  16. • Ұظઌ༧ଌͱ؍ଌ݁ՌʹΑΔϑΟϧλϦϯάΛ܁Γฦͯ͠ঢ়ଶΛܧଓతʹਪఆ • ঢ়ଶ ͸ฏۉ ͱͦͷ෼ࢄڞ෼ࢄ Ͱදݱ͢Δ͜ͱ͕Ͱ͖Δ α μ P

    36 ઢܗΧϧϚϯϑΟϧλʹΑΔ࿹ͷঢ়ଶਪఆʢ࠶ܝʣ Ұظઌͷঢ়ଶ༧ଌ Ұظઌͷ؍ଌ༧ଌ ؍ଌͷޡࠩ ϑΟϧλϦϯά ઢܗΧϧϚϯϑΟϧλʹ͓͚Δঢ়ଶߋ৽ͷαΠΫϧ t = t + 1 <latexit sha1_base64="VUdnMLAFVZPBHlSiKxWJLDz2ElQ=">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</latexit> µt+1 = Tµt|t Pt+1 = TPt|t TT + RQRT <latexit sha1_base64="HRYMQ8d6BFhrV94UjkWxn/4MPOI=">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</latexit> µt|t = µt + Kvt = µt + (PtZTF 1 t )vt Pt|t = Pt KFtKT <latexit sha1_base64="c9JcpZwYoLYc2KvKMX5kFsilLbI=">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</latexit> vt = yt ˆ yt Ft = ZPtZ T + H <latexit sha1_base64="5CGzvCsqCzyEmpk7BFtJ5+zd9FU=">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</latexit> ˆ yt = Zµt <latexit sha1_base64="sOqAisWQEAZIxvyNoh5E7NBLmlI=">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</latexit>
  17. • ઢܗΧϧϚϯϑΟϧλʹ͓͚Δߦྻ ΍ ͸ϑΟϧλϦϯά΍Ұظઌ༧ଌͷॲ ཧʹ͓͍ͯঢ়ଶͷฏۉ΍෼ࢄڞ෼ࢄͷͲͷཁૉΛߋ৽͢Δ͔ܾఆ͍ͯ͠Δ Z R 37 จ຺ʹԠͨ͡࿹ͷධՁߋ৽ Ұظઌͷঢ়ଶ༧ଌ

    Ұظઌͷ؍ଌ༧ଌ ؍ଌͷޡࠩ ϑΟϧλϦϯά ઢܗΧϧϚϯϑΟϧλʹ͓͚Δঢ়ଶߋ৽ͷαΠΫϧ t = t + 1 <latexit sha1_base64="VUdnMLAFVZPBHlSiKxWJLDz2ElQ=">AAACinichVHLSsNAFL2Nr1qrrboR3ARLRRDKpAq+EIq6cNmHfUAtJYnTOjQvkmmhFn/AnSvBrhRciB/gB7jxB1z0E8RlBTcuvE0DosV6w2TOnLnnzpm5iqUxhxPS8Qkjo2PjE/7JwFRweiYUnp3LOWbdVmlWNTXTLiiyQzVm0CxnXKMFy6ayrmg0r9T2e/v5BrUdZhpHvGnRki5XDVZhqsyRynNxV+SrUjkcITHihjgIJA9EwIukGX6EYzgBE1Sogw4UDOCINZDBwa8IEhCwkCtBCzkbEXP3KZxDALV1zKKYISNbw38VV0WPNXDdq+m4ahVP0XDYqBQhSl7IPemSZ/JAXsnnn7Vabo2elybOSl9LrXLoYiHz8a9Kx5nD6bdqqGcOFdh0vTL0brlM7xZqX984u+pmttPR1jK5JW/o/4Z0yBPewGi8q3cpmm4P8aOgF3wxbJD0ux2DIBePSWuxeGo9ktjzWuWHRViCFezHBiTgEJKQdetfwjW0haAQF7aEnX6q4PM08/AjhIMvdtyReA==</latexit> µt+1 = Tµt|t Pt+1 = TPt|t TT + RQRT <latexit sha1_base64="HRYMQ8d6BFhrV94UjkWxn/4MPOI=">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</latexit> µt|t = µt + Kvt = µt + (PtZTF 1 t )vt Pt|t = Pt KFtKT <latexit sha1_base64="c9JcpZwYoLYc2KvKMX5kFsilLbI=">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</latexit> vt = yt ˆ yt Ft = ZPtZ T + H <latexit sha1_base64="5CGzvCsqCzyEmpk7BFtJ5+zd9FU=">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</latexit> ˆ yt = Zµt <latexit sha1_base64="sOqAisWQEAZIxvyNoh5E7NBLmlI=">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</latexit> ঢ়ଶਪҠ࣌ͷޡࠩΛ෇༩ ؍ଌ࣌ͷޡࠩΛ෇༩
  18. • ઢܗΧϧϚϯϑΟϧλʹ͓͚Δߦྻ ΍ ͸ϑΟϧλϦϯά΍Ұظઌ༧ଌͷॲ ཧʹ͓͍ͯঢ়ଶͷฏۉ΍෼ࢄڞ෼ࢄͷͲͷཁૉΛߋ৽͢Δ͔ܾఆ͍ͯ͠Δ • → ଟ༷ͳจ຺Λѻ͏ઃఆͰ͸ৗʹಉ͡ߦྻΛ༻͍ͨߋ৽͸ద͞ͳ͍ Z R

    38 จ຺ʹԠͨ͡࿹ͷධՁߋ৽ Ұظઌͷঢ়ଶ༧ଌ µt+1 = Tµt|t Pt+1 = TPt|t TT + RQRT <latexit sha1_base64="HRYMQ8d6BFhrV94UjkWxn/4MPOI=">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</latexit> ঢ়ଶਪҠ࣌ͷޡࠩΛ෇༩ RQRT = 2 4 2 v 2 v 2 v 2 v 2 v 2 v 2 v 2 v 2 v 3 5 , where R = 2 4 1 1 1 3 5 , Q = ⇥ 2 v ⇤ <latexit sha1_base64="T9Wddcn++z2YoAfRJU6UFJY4tKU=">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</latexit> ഉଞతͳίϯςΩετͷ࣍ݩʹ΋ޡ͕ࠩ஝ੵͯ͠͠·͏ ίϯςΩετ"Ͱऑ͍࿹͸ɺܽଛ஋ॲཧʹΑΓଞͷίϯςΩετʹରͯ͠΋ޡࠩΛ෇༩͢Δɻ ίϯςΩετ#Ͱճఔ౓ͷ୳ࡧͰྑ͍΋ͷ͕ճ୳ࡧ͞ΕΔ͔΋͠Εͳ͍
  19. • ઢܗΧϧϚϯϑΟϧλʹ͓͚Δߦྻ ΍ ͸ϑΟϧλϦϯά΍Ұظઌ༧ଌͷॲ ཧʹ͓͍ͯঢ়ଶͷฏۉ΍෼ࢄڞ෼ࢄͷͲͷཁૉΛߋ৽͢Δ͔ܾఆ͍ͯ͠Δ • → จ຺ʹԠͨ࣌͡มͳߦྻΛ༻ҙ͢Δ Z R

    39 จ຺ʹԠͨ͡࿹ͷධՁߋ৽ Ұظઌͷঢ়ଶ༧ଌ µt+1 = Tµt|t Pt+1 = TPt|t TT + RQRT <latexit sha1_base64="HRYMQ8d6BFhrV94UjkWxn/4MPOI=">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</latexit> ঢ়ଶਪҠ࣌ͷޡࠩΛ෇༩ ίϯςΩετͷԠͨ͡  Λ༻ҙ͢Δʢ ʹ͍ͭͯ΋ಉ༷ʣ R R(xt ) Z RtQRT t = 2 4 2 v 0 2 v 0 0 0 2 v 0 2 v 3 5 , where Rt = 2 4 1 0 1 3 5 , Q = ⇥ 2 v ⇤ <latexit sha1_base64="jo6AvliL3tCEhX31/lQ29CB2t6M=">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</latexit> Rt = xt = (1, 0, 1)> (xt 2 {0, 1}m) <latexit sha1_base64="6uj048zFZHaC921ToJdOotXm6RI=">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</latexit>
  20. • ֤࣌఺ͷࢼߦ݁ՌΛɺํࡦͷ൑அʢ׆༻͔୳ࡧ͔ʣͱબఆͨ͠࿹ͷਅͷ༗༻ੑ ʢ࠷ద࿹͔Ͳ͏͔ʣͱͷ࢛৅ݶʹ෼ྨͨࠞ͠ಉߦྻʢද1ʣ 43 มԽ΁ͷ௥ैੑͱ୳ࡧޮ཰ͷࢦඪ ( ஋) F0.5 3FDBMMᶃ ᶃ

    ᶄ ൪ڰΘͤͷ৔߹ ᶄʹ૬౰͢Δࢼߦ͕ɺ৽ͨͳ࠷ద࿹ͷධՁͷ ߋ৽ʹඞཁɻ৽ͨͳ࠷ద࿹΁ͷ੾Γସ͑ʹ൐ ͍ᶅͷ૿Ճ͕ࢭ·Δ ൪ڰΘͤͰ͸ͳ͍৔߹ ᶅʹ૬౰͢Δࢼߦ͕ɺ࿹ͷධՁͷߋ৽ ͱ੾ΓସΘΓͷݕग़Λ݉ͶΔ 1SFDJTJPOᶃ ᶃ ᶅ F0.5 = 1.25 Precision ⋅ Recall 0.25Precision + Recall ͳ͓ɺᶄ͸ޡ൑ఆͰ͋Δ΋ͷͷɺ࠷ద࿹Λ બఆ͓ͯ͠Γ୹ظతͳػձଛࣦ͕গͳ͍ͨ Ί1SFDJTJPOΛॏࢹ͢Δ
  21. • ఏҊख๏Ͱ͋ΔLKF͸ঢ়ଶͷ࣍ݩ਺ΛίϯςΩετ ͱἧ͑ͨϞσϧΛར༻ • จ຺෇͖ɺ͔ͭɺඇఆৗͳํࡦͰ͋ΔDecay LinUCBɺAdTSɺdLinUCBɺ DenBandɺTVTPɺADA-ILTCB+ͱൺֱ • ͨͩ͠ɺADA-ILTCB+͸ຊઃఆʹ͓͚Δ࣮ߦ࣌ؒͷ౎߹ɺ݁Ռ͔Βআ֎ •

    ࿹ͷධՁ͕ఆ·ͬͨͷͪͷมԽ΁ͷ௥ैੑΛධՁ͢ΔͨΊ֤࿹ͷ֤ίϯςΩε τ͝ͱʹ50ճͷࢼߦ݁ՌΛ༧Ί༩͑Δ • ཚ਺Λ༻͍ͨγϛϡϨʔγϣϯ݁ՌΛฏۉԽ͢ΔͨΊ50ճͷฏۉΛ݁Ռͱ͠ ͯ༻͍Δɻ·֤ͨํࡦͷύϥϝʔλ͸ࣄલͷ༧උධՁʹΑΓྦྷੵΫϦοΫ਺͕ ଟ͍΋ͷΛબఆͨ͠ x 47 ධՁํ๏
  22. ྦྷੵϦάϨοτͷਪҠʢ্: શίϯςΩετɺԼ: ʣ x = (0,1,0,0) 48 ػձଛࣦͷධՁ • DenBand(94.3)ɺఏҊख๏ͷ

    LKF(94.8)ͱ΄΅ಉ౳ͷੑೳ • ൪ڰΘͤ΁௥ैͨ͜͠ͱͰશମ తͳϦάϨοτͷ૿ՃΛ཈͑ͨ
  23. 49 ػձଛࣦͷධՁ • ํࡦ͝ͱͷ࿹ͷબఆ਺ʹΑΔൺֱ • ࠷্ஈ͸ཧ૝తͳબఆͰͷਪҠ • Decay LinUCB͸TVTPͱɺdLinUCB͸DenBandͱಉ͡ ਪҠಛੑͷͨΊলུ

    • ͍ͣΕͷख๏΋൪ڰΘͤͰ͸ͳ͍࠷ॳͷ੾ସʹ ͸௥ैʢᒵ৭ͷ૿Ճʣ • AdTSɺTVTPɺʢDecay LinUCBʣ͸൪ڰΘͤ΁ ͷ௥ै͕஗Ε͍ͯΔʢ྘৭͕؇΍͔ʹ૿Ճʣ • DenBandɺʢdLinUCBʣɺఏҊख๏ͷLKF͸൪ ڰΘͤʹ΋ਝ଎ʹ௥ैʢ྘৭ͷٸܹʹ૿Ճʣ
  24. 50 มԽ΁ͷ௥ैੑͱ୳ࡧޮ཰ͷධՁ Ͱͷ ஋ͷਪҠʢ+: Precision,ɾ:Recallʣ x = (0,1,0,0) F0.5 •

    ఏҊख๏ͷLKF͕ߴ͍ਫ४ͰͷPrecisionͱ RecallΛཱ྆͠ɺ஋͕࠷΋େ͖͍ • = ޡ൑ఆͷظؒͱ৽ͨͳ࿹΁ͷ୳ࡧΛ࠷খݶ ʹ཈͍͑ͯΔ • ൪ڰΘͤ΁ͷ௥ै͕஗ΕͨํࡦͰ͸࠷ద࿹΁ͷ ୳ࡧᶄ͕গͳ͍ʢRecall͸େ͖͍ʣ͕ɺҎલͷ ࠷ద࿹΁ͷࢼߦᶅ͕ଟ͍ʢPrecision͕খ͍͞ʣ
  25. 51 มԽ΁ͷ௥ैੑͱ୳ࡧޮ཰ͷධՁ Ͱͷ ஋ͷਪҠʢ+: Precision,ɾ:Recallʣ x = (0,1,0,0) F0.5 •

    AdTSͰ΋൪ڰΘͤ΁ͷ௥ै͕஗ΕͨͨΊLKFΑ Γ ஋͕௿͍ɻ • ൪ڰΘͤͷݕग़ͷͨΊຫੑతʹ୳ࡧᶆ͕ଟ͍ ͜ͱ͔ΒɺશମͰͷϦάϨοτ͸૿Ճ͍ͯ͠ Δ͕มԽظؒʹ͓͚ΔੑೳΛൺֱ͢Δຊࢦඪ ͔Β͸ಡΈऔΕͳ͍ɻ → ຊࢦඪʹ͓͚ΔɺมԽͷͳ͍ظؒͷ୳ࡧޮ ཰ͷ૊ΈࠐΈ͸ࠓޙͷ՝୊ͱ͢Δ F0.5
  26. 52 มԽ΁ͷ௥ैੑͱ୳ࡧޮ཰ͷධՁ Ͱͷ ஋ͷਪҠʢ+: Precision,ɾ:Recallʣ x = (0,1,0,0) F0.5 •

    dLinUCBͱDenBandͰ͸LKFͱಉ౳ఔ౓ͷϦά Ϩοτʹ΋ؔΘΒͣLKFΑΓ΋ ஋͕௿͍ɻ • ࠷ద࿹΁ͷ୳ࡧᶄ͕ۃ୺ʹଟ͍͜ͱʹىҼ͢ Δɻ৽ͨͳ࠷ద࿹΁ͷ୳ࡧΛੵۃతʹߦ͍ͭ ͭ΋ධՁͷߋ৽͸؇΍͔ͳํࡦͱΘ͔Δ → ൪ڰΘ͕ͤ୹ظؒʹߴස౓Ͱൃੜ͢ΔΑ͏ ͳ؀ڥͰͷ՝୊͕͋ΔՄೳੑΛߟྀͨ͠஋ͱ ΈͳͤΔ F0.5 ද ᶃ ᶄ ᶅ ᶆ %FDBZ-JO6$#     "E54     E-JO6$#     %FO#BOE     5751     -,'