Economic Recommendation with Surplus Maximization

Yongfeng Zhang,QiZhao,YiZhang,DanielFriedman,MinZhang,Yiqun Liu,ShaopingMaUCSantaCruz&TsinghuaUniversity

zhangyf07@gmail.com,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,TsinghuaUniversityzhangyf07@gmail.com,http://yongfeng.me