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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/iot...

 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/

monochromegane

December 03, 2020
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  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๏
  2. • ࿹͝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
  3. • ࿹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 <latexit sha1_base64="sXrCZl7s65TuB2kkSnvZFuw+Fac=">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</latexit>
  4. • ࿹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 ◆ <latexit sha1_base64="U2Q8+JZHKTI1SORJwl0rrVRGhZw=">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</latexit> มԽલ มԽޙ
  5. • 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
  6. 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՝୊
  7. • 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 
  8. • 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՝୊
  9. • ࿹͝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
  10. • ࢼߦ࣌ͷίϯςΩετ৘ใ ͱใु ͔Β࿹͝ͱͷઢܗύϥϝʔλΛਪఆ • ίϯςΩετ৘ใͷཁҼ਺ʢ=ઢܗύϥϝʔλͷཁҼ਺ʣ͸ ࣍ݩͱ͢Δ b r d

    28 ઢܗύϥϝʔλͷਪఆ Bi = Bi + bbT <latexit sha1_base64="unbR7Yhs6Rkk/aTZ4HTBNw48AxE=">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</latexit> Bi = 0 B B B @ b11 b12 · · · b1d b21 b22 · · · b2d . . . . . . . . . . . . bd1 bd2 · · · bdd 1 C C C A <latexit sha1_base64="EnMuxPCN94aEHMciGdHB9I47X5M=">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</latexit> fi = 0 B B B @ br1 br2 . . . brd 1 C C C A <latexit sha1_base64="IJBFM+VMZa5dmBFfd6Csj18HC0o=">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</latexit> fi = fi + br <latexit sha1_base64="uZ3PwZId0gcRyzSKxEc4GfIgZug=">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</latexit> ✓i = 0 B B B @ ✓1 ✓2 . . . ✓d 1 C C C A <latexit sha1_base64="1YjVOLsXj5FWoj4jVQAS3LB2BCc=">AAAC8XichVHNShxBEK4Z498YdWMuQi6SxaCXpWcTMAiCkItHf7JqcGToma3dbez5oad3YR3mBXwBkVyikEPwAfIAXjwHcvARxKMBPXhI7eyQmEhMDTP91df11Xzd5cVSJJqxC8MceDI4NDwyao09HZ+YLD2b2kyitvKx5kcyUtseT1CKEGtaaInbsUIeeBK3vL13vf2tDqpEROF73Y1xN+DNUDSEzzVRbkk6XpA6uoWaZ65YciQ29JzleNgUYcqV4t0s9Skyq1/kpnbmOL+Sap506pFO7rF1qsawXugtR4lmS89bllsqswrLY+YhsAtQhiJWo9JXcKAOEfjQhgAQQtCEJXBI6NkBGxjExO1CSpwiJPJ9hAws0rapCqmCE7tH3yZlOwUbUt7rmeRqn/4i6VWknIFZ9p19YdfsnJ2yS3b3z15p3qPnpUur19di7E4eTG/c/FcV0Kqh9Vv1qGcNDXibexXkPc6Z3in8vr6zf3i9sbg+m75iJ+yK/B+zC3ZGJwg7P/zPa7j+8RE/HnmhG6MB2X+P4yHYrFbs15Xq2pvy8odiVCPwAl7CHM1jAZZhBVahRv2/wa1hGKaZmEfmJ/OkX2oaheY5/BHm6U8qrLo1</latexit> ✓i = B 1 i fi <latexit sha1_base64="g09wD2RSWqw0wHG2RtT4ql0+Bd4=">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</latexit> ର֯੒෼͸ͦͷཁҼͷࢼߦճ਺ɻ ͦͷଞͷ஋͸ɺର֯੒෼ͱͦͷཁҼͷ ૊Έ߹ΘͤʹΑΔࢼߦճ਺Λද͢ɻ ͦͷཁҼͷྦྷੵใुΛද͢ ͷٯߦྻͱ ͷੵΑΓཁҼ͝ͱͷઢ ܗύϥϝʔλΛਪఆ ʢཁҼ͕ഉଞͰ͋Ε͹ฏۉใुֹʣ B f
  11. 29 ઢܗύϥϝʔλͷࢦඪ • ࢦඪᶃ: ํ޲σʔλͷҟৗ౓ • 1-(ઢܗύϥϝʔλͷฏۉͱͷ ίαΠϯྨࣅ౓) • ࢦඪᶄ:

    େ͖͞ • ઢܗύϥϝʔλͷL2ϊϧϜ a = 1 (¯ ✓T✓/(||¯ ✓||2 · ||✓||2)) <latexit sha1_base64="B8copNyQgd+bR5poFPbID2QdklY=">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</latexit> m = ||✓||2 <latexit sha1_base64="dgH94A8w59qV77Hq5Q93Yg7Kh7c=">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</latexit>
  12. • ਪఆͨ͠ઢܗύϥϝʔλͷ஋ͷҟৗ౓ͱେ͖͔͞ΒඇఆৗͳมԽΛݕग़͢Δ • → ཁҼ਺ʹΑΒͳ͍ݻఆ਺ͷ஋ͷΈ͔ΒมԽݕग़ʢ ʣ • ADWINʹΑͬͯมԽΛݕग़ͨ͠৔߹ɺมԽલͷࢼߦճ਺ɺྦྷੵใुΛআڈ 2d →

    d → 2 30 ઢܗύϥϝʔλͷมԽݕग़ʢADWIN-Vʣ ✓i = B 1 i fi <latexit sha1_base64="g09wD2RSWqw0wHG2RtT4ql0+Bd4=">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</latexit> ᶄઢܗύϥϝʔλͷࢦඪ ᶅ࣌ܥྻͱͯ͠஋Λอଘ ᶆ"%8*/ʹΑΔ஋ ͷมԽݕग़ m, a ᶇมԽલͷ஋Λআڈ ᶃઢܗύϥϝʔλͷਪఆ a = 1 (¯ ✓T✓/(||¯ ✓||2 · ||✓||2)) <latexit sha1_base64="B8copNyQgd+bR5poFPbID2QdklY=">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</latexit> m = ||✓||2 <latexit sha1_base64="dgH94A8w59qV77Hq5Q93Yg7Kh7c=">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</latexit> Am = {mt 100, mt 99, · · · , mt 1} <latexit sha1_base64="jr0cSopxgsYFsCamMcfB5eWYfgw=">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</latexit> Aa = {at 100, at 99, · · · , at 1} <latexit sha1_base64="zfllfKE3yNiaBc2jNyCblYQ2HaQ=">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</latexit>
  13. • ᶃมԽݕग़ʹ༻͍Δཤྺσʔλʢཤྺظؒ x ࿹ͷ਺ʣ 32 ఏҊख๏ʹ͓͚Δཤྺσʔλ Am = {mt 100,

    mt 99, · · · , mt 1} <latexit sha1_base64="jr0cSopxgsYFsCamMcfB5eWYfgw=">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</latexit> Aa = {at 100, at 99, · · · , at 1} <latexit sha1_base64="zfllfKE3yNiaBc2jNyCblYQ2HaQ=">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</latexit> Bi = 0 B B B @ b11 b12 · · · b1d b21 b22 · · · b2d . . . . . . . . . . . . bd1 bd2 · · · bdd 1 C C C A <latexit sha1_base64="EnMuxPCN94aEHMciGdHB9I47X5M=">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</latexit> fi = 0 B B B @ br1 br2 . . . brd 1 C C C A <latexit sha1_base64="IJBFM+VMZa5dmBFfd6Csj18HC0o=">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</latexit> a = 1 (¯ ✓T✓/(||¯ ✓||2 · ||✓||2)) <latexit sha1_base64="B8copNyQgd+bR5poFPbID2QdklY=">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</latexit> m = ||✓||2 <latexit sha1_base64="dgH94A8w59qV77Hq5Q93Yg7Kh7c=">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</latexit> E(f) = {ft 100, ft 99, · · · , ft 1} <latexit sha1_base64="48SqjCY3L6okjSYu0rSeYEihhN4=">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</latexit> E(B) = {Bt 100, Bt 99, · · · , Bt 1} <latexit sha1_base64="SpKCHUMSykLNQBZgDcoIeEf627M=">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</latexit> • ᶄมԽ௥ैʹ༻͍Δཤྺσʔλʢཤྺظؒ x ࿹ͷ਺ x ࣍ݩ਺ʣ
  14. 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 …
  15. • ᶃมԽݕग़ʹ༻͍Δཤྺσʔλʢཤྺظؒ x ࿹ͷ਺ʣ 34 มԽݕग़ͷཤྺσʔλαΠζͷ௿ݮ Am = {mt 100,

    mt 99, · · · , mt 1} <latexit sha1_base64="jr0cSopxgsYFsCamMcfB5eWYfgw=">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</latexit> Aa = {at 100, at 99, · · · , at 1} <latexit sha1_base64="zfllfKE3yNiaBc2jNyCblYQ2HaQ=">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</latexit> a = 1 (¯ ✓T✓/(||¯ ✓||2 · ||✓||2)) <latexit sha1_base64="B8copNyQgd+bR5poFPbID2QdklY=">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</latexit> m = ||✓||2 <latexit sha1_base64="dgH94A8w59qV77Hq5Q93Yg7Kh7c=">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</latexit> 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
  16. 35 มԽ௥ैͷཤྺσʔλαΠζͷ௿ݮ Bi = 0 B B B @ b11

    b12 · · · b1d b21 b22 · · · b2d . . . . . . . . . . . . bd1 bd2 · · · bdd 1 C C C A <latexit sha1_base64="EnMuxPCN94aEHMciGdHB9I47X5M=">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</latexit> fi = 0 B B B @ br1 br2 . . . brd 1 C C C A <latexit sha1_base64="IJBFM+VMZa5dmBFfd6Csj18HC0o=">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</latexit> E(f) = {ft 100, ft 99, · · · , ft 1} <latexit sha1_base64="48SqjCY3L6okjSYu0rSeYEihhN4=">AAACuXichVFNSxtRFD1Oa/2obVLdCG5CQ0QhDXesUG0piFLoUo1RwYlhZvISp84XMy8BHeYP9A8UdNWCi9If0G2hm+q+C3+CuFTopgtvJgOioekdZt65591z57x3Dd+2Qkl0PqA8eDj4aGh4ZPTx2JOnmeyz8c3QawWmqJie7QXbhh4K23JFRVrSFtt+IHTHsMWWsb/S2d9qiyC0PHdDHvii6uhN12pYpi6ZqmXnNcOJ3sW70UxjNs69zWlRYzeSL1SiuJigxcW4qJl1T4bdXI21uJbNU4mSyPUCNQV5pLHqZb9DQx0eTLTgQMCFZGxDR8jPDlQQfOaqiJgLGFnJvkCMUda2uEpwhc7sPn+bnO2krMt5p2eYqE3+i81vwMocCvSbvtIV/aJvdEF//9krSnp0vBzwanS1wq9lPk6W//xX5fAqsXer6utZooGFxKvF3v2E6ZzC7Orbh5+uyq/XC9E0faFL9v+Zzuknn8BtX5sna2L9uI8fg73wjfGA1Pvj6AWbcyX1ZWlubT6/tJyOahhTeI4ZnscrLOE9VlHh/kf4gVOcKW8UXdlTPnRLlYFUM4E7oYQ3vvijlA==</latexit> E(B) = {Bt 100, Bt 99, · · · , Bt 1} <latexit sha1_base64="SpKCHUMSykLNQBZgDcoIeEf627M=">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</latexit> • ᶄมԽ௥ैʹ༻͍Δཤྺσʔλʢཤྺظؒ x ࿹ͷ਺ x ࣍ݩ਺ʣ • ࢦ਺ώετάϥϜ͸1࣍ݩͷ࣌ܥྻσʔλΛର৅ͱ͍ͯ͠Δ • 1࣍ݩ͋ͨΓ2ͭͷσʔλ͕ඞཁ
  17. 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
  18. • 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
  19. • 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