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1、ActivelyLearningHemimetricswithApplicationstoElicitingUserPreferencesAdishSinglaADISH.SINGLA@INF.ETHZ.CHSebastianTschiatschekSEBASTIAN.TSCHIATSCHEK@INF.ETHZ.CHAndreasKrauseKRAUSEA@ETHZ.CHETHZurich,SwitzerlandAbstractpreferencesofusers(e.g.,buyersorsellersinamarketplace)Motivatedb
2、yanapplicationofelicitingusers’fordifferentitems(e.g.,fromacatalogueofproducts)topreferences,weinvestigatetheproblemoflearn-improveproductrecommendationanddynamicpricinginghemimetrics,i.e.,pairwisedistancesamongaofgoods(Desjardinsetal.,2006;Horton&Johari,2015;setofnitemsthatsatis
3、fytriangleinequalitiesandBlumetal.,2015;Vazquez-Galloetal.´,2014).non-negativityconstraints.Inourapplication,theMotivatingapplications.Weareinterestedinlearningthe(asymmetric)distancesquantifyprivatecostsapreferencesofusersacrossdifferentchoicesavailableinuserincurswhensubstituti
4、ngoneitembyanother.amarketplace—thesechoicesaregivenintheformofnWeaimtolearnthesedistances(costs)byasking(typesof)items.Forinstance,inarestaurantrecommenda-theuserswhethertheyarewillingtoswitchfromtionsystemsuchasYelp,theitemtypescouldcorrespondtooneitemtoanotherforagivenincentiv
5、eoffer.restaurantsabstractedbyattributessuchascuisine,locality,Withoutexploitingstructuralconstraintsofthereviewsandsoon.Considerauserwhoseeksrecommenda-hemimetricpolytope,learningthedistancesbe-tionsfromthesystemandhaschosenitemi(e.g.,“Mexicantweeneachpairofitemsrequires(n2)que
6、ries.restaurantinManhattanwithover50reviews”).However,Weproposeanactivelearningalgorithmthattoincentivizeexplorationandmaximizeitsoverallutility,substantiallyreducesthissamplecomplexitybythemarketplacemayconsiderofferingadiscounttotheexploitingthestructuralconstraintsontheversion
7、usertoinsteadchooseitemj(e.g.,“Newlyopenedfastfoodspaceofhemimetrics.OurproposedalgorithmrestaurantinNewJerseywith0reviews”),e.g.,togatherachievesprovably-optimalsamplecomplexityformorereviewsforitemj.Thepriceoftheofferwouldclearlyvariousinstancesofthetask.Forexample,whendependon
8、howsimilarordissimilarthechoicesiandjare
