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Review: “Real-Time Bidding Algorithms for performance-Based Display Ad Allocation” Tatsuki Sugio

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ຊ࿦จͷ֓ཁ A. demand-side, supply-side • ༧ࢉ౤ࢿͷ࠷దԽɺऩӹʢrevenueʣͷ࠷େԽ • RTB Exchangeʹ͓͍ͯɺimpຖʹΩϟϯϖʔϯΛׂΓ౰ͯΔ ➡ ϦΞϧλΠϜͰͷ࠷దԽʹΑΓ࣮ݱ ➡ errorͷେ͖͞ʹԠͯ͡ύϥϝʔλΛௐ੔
 B. ՝୊ • ม਺ɺ੍໿͕ଟ͍ ➡ ઢܗܭը໰୊ͷ૒ର໰୊ͷղʹΑΓ࣮ݱ • ΦϑϥΠϯ࠷దԽͰ͸ཻ౓͕ૈ͍
 ࢢ৔ͷมԽʹରͯ͠దԠతͳbid͕Ͱ͖ͳ͍ ➡ ϦΞϧλΠϜͰͷ࠷దԽʹΑΔࡉཻ͔͍౓Ͱͷ࠷దԽΛ࣮ݱ
 C. ํ๏ • online bidding algorithm frameworkΛఏҊ • Ωϟϯϖʔϯຖͷbidػೳύϥϝʔλͷߋ৽ํ๏ʢWaterlevel or Model-based ʣͱͯ͠ɺطଘͷϦιʔε഑ ෼ͷۙࣅΞϧΰϦζϜʹinspire͞Εͨํ๏ͱɺbidͷউ཰ͷ෼෍ΛϞσϧԽͯࣜ͠ʹ૊ΈࠐΜͩ΋ͷΛఏҊɻ

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Formulation A. ऩӹͷఆٛ
 
 
 
 
 B. ೖࡳֹͷܾఆɺௐ੔ ޿ࠂओผ ೖࡳֹௐ੔ͷ߲ ͜Ε͔Β͜ͷzЋzΛٻΊͯɺ࠷దͳzCJEQSJDFzΛਪఆ͠·͢

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LR Formulation • ࠷దԽ໰୊ ΩϟϯϖʔϯKͷJ൪໨ͷJNQνϟϯεʹJNQͰ͖͔ͨ൱͔ʢೋ஋ʣ WJKQJK RJKˡ $53 $1$ ΩϟϯϖʔϯKͷ໨ඪJNQ਺ʢ༧ࢉ੍໿Λ݉ͶΔʣ εϥοΫ৚݅

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• ࠷దԽ໰୊ͷ૒ର໰୊
 
 
 
 
 
 
 
 
 ➡ α,βΛٻΊΔ͜ͱ͕໨త
 ܭࢉճ਺͸ɺO(mn)Ͱ͸ͳ͘ɺO(m+n) ➡ શϢχϞδϡϥߦྻʢtotally unimodular matrix, TU ߦྻʣʹجͮ͘
 ࢀߟʣhttp://ja.wikipedia.org/ ๚໰ऀ਺ͷ૿Ճ౳ͷܦࡁత܎਺ʢJNQͷ࠷খՁ֨ͱ΋ʣ ༧ࢉͷ૿Ճ౳ͷܦࡁత܎਺ʢ࠷খརӹͱ΋ʣ

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Real-Time Bidding Algorithm • ٙࣅίʔυ HPBMBDIJFWFE Ќͷܭࢉ POMJOF"MHPSJUINͷద༻

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Control-theoretic Bid Adjustment • waterlevel-base update (online algorithm) - ίετ͸ߟྀ͠ͳ͍ - PIɺPIDཧ࿦ JNQ਺ FSSPS FSSPSʹͲΕ͚ͩૣ͘൓Ԡ͢Δ͔ͷ܎਺

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1*%੍ޚཧ࿦ 1*%੍ޚͷجຊࣜ͸ɺภࠩFʹൺྫ͢Δग़ྗΛग़͢ൺྫಈ࡞ʢ1PQPSUJOBMBDUJPO1ಈ࡞ʣͱɺ
 ภࠩFͷੵ෼ʹൺྫ͢Δग़ྗΛग़͢ੵ෼ಈ࡞ʢ*OUFHSBMBDUJPO*ಈ࡞ʣͱɺ ภࠩFͷඍ෼ʹൺྫ͢Δग़ྗΛग़͢ඍ෼ಈ࡞ʢ%FSJWBUJWFBDUJPO%ಈ࡞ʣ͔ΒͳΔɻ ௨ৗ͸ɺ1ಈ࡞Λओମʹͯ͠ɺิॿతʹ*ಈ࡞ͱ%ಈ࡞Λ੍ޚର৅ʹԠͯ͡ద౰ʹ૊Έ߹ΘͤΔɻ
 ૢ࡞ྔ.7͸ɺͦΕͧΕͷ࿨ͱͯ͠ɺ࣍ࣜͷ༷ʹද͞ΕΔɻ IUUQXXXOJDPNXIJUFQBQFSKB

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Model-based Bid Adjustment • γεςϜ੍ޚཧ࿦ʹجͮ͘Ξϓϩʔν(PI:online algorithm) - ίετɺೖࡳֹߟྀ FSSPSʹૣ͘ͲΕ͚ͩૣ͘൓Ԡ͢Δ͔ͷ܎਺ ཧ૝తͳೖࡳՁ֨ ཧ૝తͳউ཰ʢHJʹ߹ΘͤΔͨΊʹඞཁͳউ཰ʣ ؍ଌ͞Εͨউ཰ ೖࡳίετ .-&ͷ෼෍ύϥϝʔλɻ XJOͨ͠ೖࡳ X ͷ౷ܭྔ͔Βಋ͔ΕΔɻ

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a Practical formulation • ίετ߲ͷಋೖʹΑΓߋʹҰൠԽͨ͠ओ໰୊
 
 
 
 
 
 
 
 • ίετ߲ͷಋೖʹΑΓߋʹҰൠԽͨ͠૒ର໰୊ JNQ(SPVQ QMBDFNFOU Jͷ֫ಘͰ͖ͦ͏ͳJNQ਺

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Experiments • ࣮ݧ݁Ռͷ֓ཁ - αͷௐ੔ʹΑͬͯೖࡳͷ࠷దԽ͕ߦ͑Δ͔Ͳ͏͔ - ҟͳΔ࠷దԽख๏ͷಋೖʹΑΓͲͷఔ౓ύϑΥʔϚϯε͕ҟͳΔͷ͔ - αͷॳظ஋͕Ͳͷఔ౓Өڹ͢Δͷ͔
 • ࣮ݧ৚݅ - ࢖༻σʔλ͸σΟεϓϨΠωοτϫʔΫͷσʔλ - ฏۉ1೔20Mͷimp͕͋ΔαΠτͰ࣮ݧ - 4ͭͷCPCΩϟϯϖʔϯ͕ର৅
 • σʔλ • timestamp,placement,user,campaign,clicks,impressions • ॱʹt,i=(placement:user),j,cij(t),xij(t)

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MJGU஋ ʹ ࢪࡦΛ࣮ࢪ͠ͳ͍࣌ͷ݁Ռ ࢪࡦΛ࣮ࢪͨ࣌͠ͷ݁Ռ IUUQXXXBMCFSUDPKQUFDIOPMPHZDSNMJGUIUNM

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- Experiments 1 • ؍ଌ஋ͱγϡϛϨʔγϣϯʹΑΔ஋ͷlift ➡ offlineͷΈΑΓ΋onlineͰαΛௐ੔ͨ͠ํ͕੒੷͕ྑ͍
 
 
 
 ➡ model-based bid ͱ Waterlevel bidͷൺֱ - offlineͰͷαͷࢉग़͸1೔෼ͷσʔλ - αࢉग़ޙͷ4೔ؒͷσʔλΛൺֱ ➡ online algorithm͸offline algorithmʹରͯ͠90ˋҎ্ͷ੒੷ ➡ ҆ఆੑ͸Model Bidder͕ྑ͍

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- Experiments 2 • hourlyͷ਺஋มಈʢ୹࣌ؒͷ҆ఆੑ֬ೝʣ ➡ Waterlevel Bidder͸࣌ؒతͳ҆ఆੑ͕ߴ͍ ➡ Model Bidder͸ෆ҆ఆ

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- Experiment 3 • online algorithm(Waterlevel Bidder)ʹ͓͚Δαͷॳظ஋ͷӨڹ ➡ ॳظ஋ͷมಈ͸΄ͱΜͲͳ͍
 ͔͠͠ɺΩϟϯϖʔϯ༧ࢉͷ੍໿͕ݫ͚͠Ε͹Өڹ͕͋Δ͔΋…

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• ༧ࢉ੍໿ʢݫʣ
 ➡ ༧ࢉ੍໿͕ݫ͚͠Ε͹ɺ
 ॳظ஋ͷมಈ͸͋Δɻ
 offline࠷దԽͨ͠αͷ੒੷͕ྑ͍ɻ - Experiments 4

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Conclusion • ݁࿦ - γϯϓϧ͕ͩཧ࿦తഎܠͷ͋Δonline algorithmΛఏҊ - PIDཧ࿦ͷԠ༻Մೳੑ - ଞͷछྨͷϞσϧ΋ߟྀ͢Ε͹ɺߋʹվྑ͕ग़དྷΔͷͰ͸ͳ͍͔