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1、AdaptiveMCMCwithBayesianOptimizationNimalanMahendranZiyuWangFirasHamzeNandodeFreitasUBCUBCD-WaveSystemsUBCAbstractousadaptiveMCMCmethodsfortworeasons.Firstly,theycanbeshowntobetheoreticallyvalid.Thatis,theMarkovchainismadeinhomogenousbythede-Thispaperproposesanewrandomizedstrat-pendenceoftheparame
2、terupdatesuponthehistoryegyforadaptiveMCMCusingBayesianop-oftheMarkovchain,butitsergodicitycanbeensuredtimization.Thisapproachappliestonon-(Andrieu&Robert,2001;Andrieu&Moulines,2006;differentiableobjectivefunctionsandtradesSaksman&Vihola,2010).Forexample,Theorem5offexplorationandexploitationtoreduce
3、ofRoberts&Rosenthal(2007)establishestwosimplethenumberofpotentiallycostlyobjectiveconditionstoensureergodicity:(i)thenon-adaptivefunctionevaluations.Wedemonstratethesamplerhastobeuniformlyergodicand(ii)thelevelstrategyinthecomplexsettingofsamplingofadaptationmustvanishasymptotically.Thesecon-fromc
4、onstrained,discreteanddenselycon-ditionscanbeeasilysatisfiedfordiscretestatespacesnectedprobabilisticgraphicalmodelswhere,andfiniteadaptation.foreachvariationoftheproblem,oneneedstoadjusttheparametersoftheproposalSecondly,adaptiveMCMCalgorithmsbasedonmechanismautomaticallytoensureefficientstochasticap
5、proximationhavebeenshowntoworkmixingoftheMarkovchains.wellinpractice(Haarioetal.,2001;Roberts&Rosen-thal,2009;Vihola,2010).However,therearesomelimitationstothestochasticapproximationapproach.1IntroductionSomeofthemostsuccessfulsamplersrelyonknow-ingeithertheoptimalacceptancerateorthegradientAcommo
6、nlineofattackforsolvingproblemsinofsomeobjectivefunctionofinterest.Anotherdisad-physics,statisticsandmachinelearningistodrawvantageisthatthesestochasticapproximationmeth-samplesfromprobabilitydistributionsπ(·)thatareodsmayrequiremanyiterations.Thisisparticularlyonlyknownuptoanormalizingconstant.Ma
7、rkovproblematicwhentheobjectivefunctionbeingopti-chainMonteCarlo(MCMC)algorithmsareoftenthemizedbytheadaptationmechanismiscostlytoevalu-preferredmethodforaccomplishingthissamplingtask,ate.Finally,gradientapproach
