Offline A/B testing for Recommender Systems

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Offline A/B testing for Recommender Systems ͸ͯͳ ాத (alpicola) @ ࿦จಡΈձ 11/19 1

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Ofﬂine A/B testing for Recommender Systems — CriteoͷWSDM'18ͷ࿦จ — SpotifyͷRecSys'18࿦จͰ΋ݴٴ 2

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Ofﬂine A/B testing for Recommender Systems — CriteoͷWSDM'18ͷ࿦จ — SpotifyͷRecSys'18࿦จͰ΋ݴٴ — ΫοΫύου։࠵ͷಡΈձͰ͢Ͱʹ঺հ͞Ε͍ͯͨ — ͕ɺվΊͯ۷ΓԼ͛ͨ࿩͕Ͱ͖Ε͹ͱࢥ͍·͢ 3

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ΦϑϥΠϯABςετ? — ΦϯϥΠϯͰߦ͏ABςετ͸࣌ؒͱ͕͔͔ۚΔ — ΦϑϥΠϯͰͦΕʹ͍ۙධՁ͕ߦ͑Ε͹ΞϧΰϦζ ϜվળͷαΠΫϧΛߴ଎ԽͰ͖Δ — Ͱ΋ਫ਼౓͸? ! 4

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ϩάʹجͮ͘ΦϑϥΠϯධՁͷݚڀ — Counterfactual estimationͱ͔off-policy estimationͱ ݺ͹ΕΔ — WSDM'15ͷνϡʔτϦΞϧ — SIGIR'16ͷνϡʔτϦΞϧ — ධՁ͚ͩͰͳֶ͘शͷ໨తؔ਺ʹ࢖͏͜ͱ΋Ͱ͖Δ — ͜ͷ࿦จͰ͸ධՁͷΈΛѻ͏ 5

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࿦จͷߩݙ — ΦϑϥΠϯABςετͰ༻͍Δใुͷਪఆख๏NCISͷ ͋Δछͷ࠷దੑΛࣔ͢ — ͜ͷ஌ݟʹج͍ͮͯNCISͷ֦ுPieceNCISͱ PointNCISΛఏҊ — ΦϯϥΠϯABςετ݁Ռͱͷ૬͕ؔେ͖͘޲্ 6

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໰୊ઃఆ — Top-k ϥϯΩϯά — : ϩά — : ίϯςΩετ — : ΞΫγϣϯ — : ใु 7

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໰୊ઃఆ — : ίϯςΩετ͔ΒΞΫγϣϯΛબͿϙϦγʔ — : ݱߦͷϙϦγʔ — : ςετ͍ͨ͠ϙϦγʔ — : ฏۉॲஔޮՌ — ͜ΕΛਪఆ͍ͨ͠ 8

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໰୊ઃఆ — ΦϯϥΠϯABςετ — ͷݩͰͷϩάͱ ͷݩͰͷϩά͕͋Δ — ඪຊฏۉͰ , ͦΕͧΕਪఆ — ΦϑϥΠϯABςετ — ͷݩͰͷϩά͔Β ΋ਪఆ ! 9

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ैདྷख๏ — Importance sampling (IS) — Normalized importance sampling (NIS) — Doubly robust estimator (DR) — Capped importance sampling (CIS) — Normalized capped importance sampling (NCIS) ౷ܭ΍ϞϯςΧϧϩ๏ͷจ຺Ͱొ৔ 10

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Importance sampling (IS) — ! όΠΞε͕ͳ͍ — — " ʹΑΔߴόϦΞϯε (unbounded) — όϦΞϯε͕େ͖͍ͱ ͱ ΛൺֱͰ͖ͳ͍ 11

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Normalized importance sampling (NIS) Λ࢖ͬͯ Λஔ͖׵͑ — ! ҰகਪఆྔʹͳΔ — — " ґવͱͯ͠όϦΞϯεେ 12

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Capped importance sampling (CIS) ॏΈͷ࠷େ஋Λ ʹ (max capping) ॏΈ͕ Ҏ্ͷ߲͸ࣺͯΔ (zero capping) 13

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CISͷόΠΞε 14

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CISͷόΠΞε — όΠΞε͸ ͷ࣌ͷ Ͱbound͞ΕΔ — — ͸ใु͕େ͖͍ͱ͜ΖΛऔΕΔΑ͏ʹվળ͍ͨ͠ ͕ͦ͏͢ΔͱόΠΞε͕େ͖͘ͳΔ ! 15

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CISͷόΠΞε Cappingͷઃఆʹ͍͍τϨʔυΦϑ͕ଘࡏ͠ͳ͍ ! 16

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Normalized capped importance sampling (NCIS) NIS, CIS྆ํͷΞΠσΞΛ࣋ͪࠐΉ 17

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NCISͱCISͷؔ܎ 18

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NCISͱCISͷؔ܎ CIS͕͍࣋ͬͯͨόΠΞε Λୈೋ߲ͰϞσϧ ͍ͯ͠ΔͱݟͳͤΔ 19

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NCISͱCISͷؔ܎ (ಛʹzero cappingͷ࣌) 20

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NCISͱCISͷؔ܎ (ಛʹzero cappingͷ࣌) — ͳΒ઴ۙతʹόΠΞ ε͕ͳ͘ͳΔ ! — ͷ , ʹର͢Δґଘ౓͕খ͍࣌͞ͳͲ 21

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NCISͷόΠΞε 22

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NCISͷόΠΞε — ͱcappingͷ༗ແʹ૬͕ؔ͋ΔͱόΠΞε͕େ͖͘ ͳΔ ! — ަབྷҼࢠ͸ϢʔβʔͷλΠϓͳͲ͕ߟ͑ΒΕΔ (Table 1) 23

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NCISͷόΠΞε 24

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࿦จͷΞΠσΞ — ͷϞσϦϯάΛάϩʔόϧ㱺ϩʔΧϧʹ — ίϯςΩετ ʹରͯ͠ہॴతͳNCIS — ͱcappingͷ૬ؔΛݮΒ͢ — Piecewise NCIS: ෼ׂ͞ΕͨྖҬ͝ͱʹNCIS — Pointwise NCIS: ཁૉ͝ͱʹNCIS 25

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Piecewise NCIS (PieceNCIS) ίϯςΩετͷू߹ ͷ෼ׂ Λߟ͑Δ 26

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Piecewise NCIS (PieceNCIS) ֤෼ׂʹରͯ͠NCIS 27

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෼ׂͷྫ ద౰ͳؔ਺ ΛఆΊͯ ֤ ಺Ͱ ͷ ʹର͢Δґଘ͕খ͘͞ͳΔΑ͏ʹ 28

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Pointwise NCIS (PointNCIS) ཁૉ୯ҐͰ෼ׂ͢Δ (i.e. ) ಛఆͷίϯςΩετʹର͢Δαϯϓϧ਺͸͘͝গͳ͍ͷ Ͱૉ๿ʹNCISΛద༻Ͱ͖ͳ͍ 29

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Pointwise NCIS (PointNCIS) — ͸ΞΫγϣϯʹ͍ͭͯपลԽ͢Δ ͱਖ਼֬ʹٻΊΒΕΔ — ΞΫγϣϯͷ਺͕ଟ͍ͱܭࢉ͕ߴίετ ! — ΛαϯϓϦϯάͰٻΊΔ 30

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Midzuno-Sen method 1. Λαϯϓϧ 2. Λ ͔Β ͳ΋ͷ͕ಘΒΕΔ·Ͱαϯϓϧ 3. Λ ͔Βαϯϓϧ 4. Λฦ͢ ͜͏ͯ͠ಘΒΕΔ஋Λ ͱॻ͘ 31

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Pointwise NCIS (PointNCIS) — ͷ͏ͪ ͕ ͷσʔλ͸ແࢹͰ͖Δ — ใु͕εύʔεͳ࣌ʹޮ཰తʹܭࢉͰ͖Δ ! 32

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࣮ݧ — ϓϩϓϥΠΤλϦͷσʔληοτ — 39छɺ߹ܭͰ਺ઍԯ݅ͷϩάσʔλ — ΫϦοΫϕʔεͷใु (εύʔε͔ͭ෼ࢄେ) — ର৅͸CIS, NCIS, PieceNCIS, PointNCIS ( ) — IS, NIS͸όϦΞϯε͕ߴ͗͢ΔͷͰআ֎ 33

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ΦϯϥΠϯʗΦϑϥΠϯABςετͷ૬ؔ 34

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ద߹཰ͱِӄੑ཰ ʮ ͕ ΑΓΑ͍͔Ͳ͏͔ʯͷ2஋༧ଌͱͯ͠ݟΔ 35

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࣮ݧ݁Ռͷ·ͱΊ — CIS͸૬͕ؔෛ — શମతʹ௿Ίͷਪఆ͕ग़͍ͯͨ (Figure 4) — CIS⇒NCISͰେ͖͘վળ — NCIS⇒PointNCISͰِཅੑ཰͕͞ΒʹԼ͕Δ — ద߹཰͸NCISҎޙͦ͜·ͰΑ͘ͳΒͳ͍ — ࣮ߦ଎౓ʹ͓͍ͯ΋ਫ਼౓ʹ͓͍ͯ΋PointNCIS͕Α͍ 36

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Appendix — ͕খ͍͞ͱ ͕ cappingΛ௒͑Δ͜ͱ΋ — Max cappingͰ͸ ʹͳΔΑ͏ͳ ৽͍͠capping ͕ͱΕΔ (Lemma A.3) 37