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Economic Recommendation with Surplus Maximization
Yongfeng Zhang,QiZhao,YiZhang,DanielFriedman,MinZhang,Yiqun Liu,ShaopingMaUCSantaCruz&TsinghuaUniversity
[email protected],http://yongfeng.me
Outline• BackgroundandMotivation• ProblemDefinition• TotalSurplusMaximizationFramework• ModelSpecification– E-commerce– P2Plendingservices– Onlinefreelancingplatforms
• EmpiricalAnalysisResults• ConclusionsandFutureWork
HumanActivitiesfromOfflinetoOnline• Weareexperiencingthehistoricmomentof“Onlinization”– Moreandmorehumanactivitiesaremovingfromofflinetoonline
Conductsocialingandmakefriendsonlinebysocialnetworks
PurchaseonlinebyE-commerceWebsites
Manageassetpropertiesonlineby,e.g.,P2PLendingservices
Workandmakemoneyonlinebyonlinefreelancingnetworkservices
WebApplicationsasEconomicSystem• TheWebisawholeEconomicSystemforvarioushumanactivities– Justasourofflinephysicalworld
• Involvesinteractionsoftwopartiesonsometypeofonlineservices– Consumer– OnlineServices– Producer– E-commerce:Customers– Goods– Retailors– P2Plending:Lenders– Financialproducts(loanrequests)– Borrowers– Onlinefreelancing:Employees– Jobs– Employers– Socialnetworks:You– Information(news/tweets/status)– Friends
OnlineServiceAllocation• Fundamentaltask:OnlineServiceAllocation(OSA)– Assignonlineservices(products,loans,jobs)fromproducerstoconsumersaccordingtosomeprinciples
– MainlyachievedbyRecommenderSystems• Consumersaregrantedbylawtochoosefreely• Canonly‘recommend’specificservicesfromproducertoconsumer
• Existingmethods– Usuallyaimatmaximizingthebenefitsofoneside
• E.g.,E-commerce:matchuserpreferenceandboostusersatisfaction• P2Plendingservices:recommendtomaximizelenderprofits
WebIntelligenceforSocialGood• Maybeproblematic– Asystemshouldbenefitbothpartiestobesustainable
• WebIntelligencefor SocialGood– Economists,philosophers,andsociologistsdevotetheirlivesforabetteroffinhumansocietyofourphysicalworld
–Weascomputerscientistsshouldalsopushthevirtualonlinesocietytowardsamorefair,justandwin-winworld
• TheconceptofSocialSurplus– Toachievethisgoal,weintroducetheconceptofsocialsurplusasthemetricforevaluatingandoptimizingonlineserviceallocations
ProblemDefinition• Consumers,Producers,andGoods
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ProblemDefinition• ServiceQuantityVector
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ProblemDefinition• OnlineServiceAllocation(OSA)
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Various PrinciplesforOSA• VariousPrinciplesforOSA– MaximizeUserPreference?– MaximizeProviderProfit?– MaximizetheTotalSocialSurplusforSocialGood!• Andfantasticthingshappenbeyondexpectation• Socialgood->perusersatisfaction+socialbetteroff
BasicConcepts:UtilityandSurplus• Utility– Basisofmoderneconomics– Measuresone’spreference/satisfactionoversomesetofgoods/services– Usuallyafunctionofquantityq:U(q)– GovernedbytheLawofDiminishingMarginalUtility• Asapersonincreasestheconsumptionofaproduct,thereisadeclineinthemarginalutilitythatthepersonderivesfromconsumingeachadditionalunit.• Mathematically:U(0)=0&U’(q)>0&U’’(q)<0• Consumethefirstsliceofbreadvs.Consumingthelastslicewhenfeelingfull
BasicConcept:Utility• Utility– frequentlyusedforms:– EconomistsintroducedvariousfunctionalformsforUtility– TheKPR(log)Utilityfunction
• U(0)=0&U’(q)>0&U’’(q)<0
• PersonalizedUtility– onConsumertoGoodlevel
– aij asparameterofcurvelift
BasicConcept:Surplus• Surplus– Surplusisthenetbenefit(indollarterms)associatedwithbuyingorsellingsomegood
– ConsumerSurplus(CS)• Theamountofutilityoneexperiencesbeyondthepricethatshepays
– ProducerSurplus(PS)• Theprofit:oneearnsbeyondthecost
– TotalSurplus(TS)
DirectTotalSurplusMaximization• DirectTotalSurplusMaximization(TSM)
– 1 isacolumnvectorof1’s• Sumofquantityforeachproduct(columnsuminQ)doesnotexceedmaximalamountcanbeprovided(byM)
– S:ThesetofpossiblelegalvaluesforQundergivenapplication• e.g.,S=Nfore-commerce,S={0,1}foronlinefreelancing
DirectTSM– Drawbacks• DrawbacksofDirectTSM– TheHypothesisofRationalManmaynotalwayshold– DifficulttomodelthenoisydataifwerestrictQtoexactvalues
• RelaxtheModel– RelaxQij inQtorandomvariablesforquantitydistributions– E.g.,Qij ∼ N(μij ,σij ),consumeru_i choosesgoodg_j onquantityμijforthehighestprobability,butmayalsowithotherquantities.
TotalSurplusMaximization– theFramework• Maximizetheexpectedtotalsurplus– Ourfinalframeworkforserviceallocationmaximizesthefollowingexpectedtotalsurplus:
– p(Qij)istheprobabilisticdensityfunctionofeachquantityQij
• ModelOutput– Themodeloutputstheoptimaldensityfunctionsp(Q)–Wetaketheexpectation asthefinalallocationmatrixtomakerecommendationdecisions.
ExpectedtotalsurplusforEachuser-productpair
ModelSpecificationinDifferentApplications• ModelSpecification– Differentchoicesoftheparametersfordifferentapplicationscenarios– Andalsodifferentmethodsforparameterestimation
• ModelSpecificationinthiswork– E-commerce– P2PLending– OnlineFreelancing
ModelSpecification– E-commerce• EstimationofpersonalizedutilityUij(q)– Uij (q)issubjecttotheLawofZeroSurplusfortheLastUnit
–Where:
• Thenweneedtoestimateaij– Let
ModelSpecification– E-commerce• EstimationofPersonalizedUtility byMaximumLikelihood
• ModellearningwithGradientDescent–Wehave
SigmoidProbability
ModelSpecification– E-commerce• Costfunctionandquantitydistribution– Constantper-productcostcj,sothecostfunctionis– LetQij inallocationmatrixQfollowaPoissondistribution• BecauseQij∈ N
• SpecificationofTSMforE-commerce:
– ConstraintsareleftoutbecauseMj=∞
ModelSpecification– E-commerce• Costfunctionandquantitydistribution– Constantper-productcostcj,sothecostfunctionis– LetQij inallocationmatrixQfollowaPoissondistribution• BecauseQij∈ N
• SpecificationofTSMforE-commerce:
– ConstraintsareleftoutbecauseMj=∞
・Quantityregularizer toguidethemodel learning・ λij isthequantityexpectationunderPoissondistribution・ Guide themodel learning:predictedquantitiesdonotbiastoomuch
fromobservedvaluesintrainingset.
ExpectedtotalsurplusunderPoissondistribution
ModelSpecification– P2PLending• Consumer(Lender)andProducer(Borrower)Surplus– rj:theactualinterestrateofthejth loanrequest– r:theriskfreeinterestrate(bysavingthemoneyinbank)– rjmax:themaximumacceptableinterestrateofthejth loanrequest
Interestobtainedfromtheloan– riskfreeinterest(opportunitycost)ForLenderi onloanj
Forborroweronloanj
Thehighestpossibleinterestborrowerwouldliketopay– actualinteresthehastopay
ModelSpecification– P2PLending• ProbabilisticPriorofQij
– Qij (thequantityofmoney)isacontinuousvariable:normaldistribution
• OSAformalizationforP2P
ModelSpecification– P2PLending• ModelSimplification
• Intuition– Allocatetheinvestmentsinagreedymanneraccordingtothepercapitasurplus(rmax−rˆ)ofeachloanrequest
– Anintuitionalruleforinvestmentinpractice
ModelSpecification– OnlineFreelancing• UtilityandCost– Firstpredictemployee-jobandemployer-job ratingsthroughCF– Assumption:percentagesurplusagainstpriceisproportionaltosigmoid-normalizedratings
– Qij∈{0,1}becauseajobcanbeprovidedonlyonce• canbeviewedasanindicatorofwhetherornotajobisassigned
• RepresentationofSurpluses
ModelSpecification– OnlineFreelancing• ProbabilisticPriorofQij
– Qij isbinaryvalued:Bernoullidistribution
• Quantityconstraint:– Mj=1becauseeachjobcanbyprovidedandonlyonce
• ModelSpecification:Jobassignment:
EmpiricalAnalysis– E-commerce• Dataset– Shop.com
– Eachtransection• ConsumerandProductID• Price oftheproduct,andPurchasingquantity
– TrainingandTestingset• Foreachconsumer,randomlyselect25%transactionsastestingset
EmpiricalAnalysis– E-commerce• ExperimentalSetup– TSMgivesestimatedvaluesofQij
– ProductrecommendationlistoflengthNisprovidedtoconsumeruibyrankingtheproductsindescendingorderofQij
– Baselinemethod• CollaborativeFiltering:
• Evaluationmetrics– ConversionRate@N(CR@N)• Forrecommendationperformance
– TotalSurplus@N(TS@N)• Foreconomicperformance
Qij
EmpiricalAnalysis– E-commerce• ConversionRate– Underdifferentη selections, constantlybetterthanCF
EmpiricalAnalysis– E-commerce• ConversionRate– Underdifferentη selections,constantlybetterthanCF
Smallerη‘sgainbetterconversionrateunder longrecommendation lists
Surpluscomponent takescontrolofrecommendationperformanceunder longrecommendations
Largerη‘sgainbetterconversionrateundershortreclists
Weneedstrongquantityregularizerstoguaranteequalityofthetopseveralrecommendations
EmpiricalAnalysis– E-commerce• TotalSurplus– ConstantlybetterthanCFunderdifferentη selections
EmpiricalAnalysis– E-commerce• TotalSurplus– ConstantlybetterthanCFunderdifferentη selections
Smallerη‘sgainbettertotalsurplus
Notsurprising becausethetotalsurpluscomponentbynaturetriestomaximizetotalsurplus
EmpiricalAnalysis– E-commerce• Details
• Conclusion– Higherconversionrate(recommendationperformance)– Highertotalsurplus(socialgood)– TheTSMframeworkimprovesrecommendationexperienceofusers• Althoughwemaximizethebenefitsofbothsidesjointly
– Benefitssocialgoodatthesametime
EmpiricalAnalysis– P2PLending• ProsperDataset– November9th2005toMay8th2009 (automaticbiddingafterwards)– Statistics
• Evaluation– TotalSurplus(TS)
EmpiricalAnalysis– P2PLending• EvaluationProtocol– ComparetheTotalSurplusbetweenourallocationandtheactualallocation
• 34.42%highertotalandperlisting/capitasurplus• From$0.16percapitato$0.21percapita
– Anexcitingimprovementincapitalefficiencyandsocialgood
EmpiricalAnalysis– OnlineFreelancing• Dataset– ZBJfreelancingplatformdataset(http://zbj.com)• AChineseonlinemarketingwebapplications
• Baseline– Constructthefreelancer-jobratingmatrixandconductCF• Holdout25%ratingsfortesting
– Assignajobtothefreelancerwiththehighestpredictedrating
EmpiricalAnalysis– OnlineFreelancing• Evaluationmetrics– ConversionRate(%ofproperlyassignedjobs)– TotalSurplus
• Resultsunderdifferent#offactorizationfactorsK– CR@K
– TS@K
– BetterCRandTSthanCF,andbetterTSeventhantheactualallocation• ¥73.13/jobforTSMwhenK=30,only¥31.37/jobfor CF and¥43.74/jobfor actual• Bettermarketefficiency
Conclusions• Conclusions–Webasonlineeconomicsystemwithinteractionofproducersandconsumers– PromoteWebIntelligenceforSocialGoodbydirectsocialgoodmetricmaximization,forabetteroffofthewholeonlinesystem
– ProposeaTotalSurplusMaximization(TSM) framework– Thisframeworkcanbespecifiedtovariousreal-worldapplications– Resultsshowthatbymaximizingthetotalsurplus,wecanbenefituserexperienceandsocialgoodatthesametime
FutureWork- More• AnewangletoviewtheWeb– Fromaconsumer-producerperspectiveofview– AndmaximizingthetotalsurplusforabetteroffoftheWeb
• OthermodelspecificationsbeyondEC,P2P,freelancing– Socialnetworks,crowdsourcing,Uber,Airbnb,etc.
• OtherpossibledirectionsbeyondEconomicRecommendation– EconomicIR fromacooperativesocialgoodperspective– DynamicpricingforsocialgoodmaximizationinE-commerce,drivingservices(Uber),Rentalservices(Airbnb),etc.
Yongfeng Zhang,[email protected],http://yongfeng.me