On-line Optimization of Sequential Monte Carlo Methods

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1、ProceedingsoftheAmericanControlConferenceAnchorage,AKMay8-10.2002On-lineOptimizationofSequentialMonteCarloMethodsusingStochasticApproximationArnaudDoucet’,VladislavB.TadiCDepartmentofElectricalandElectronicEngineering,TheUniversityofMelbourne,Parkville,Victoria305

2、2,Australia.Email:{a.doucet,v.tadic}Qee.mu.oz.auAbstractderweakassumptions,itcanbetypicallyshownthatthesealgorithmsconvergeinacertainsensetowardstheSequentialMonteCarlo(SMC)methodsakaParticleposteriorprobabilitydistributionsofinterestasymp-ateringtechniquesareaset

3、ofpowerfulandversatiletoticallyinthenumberofparticles[5],[SI.However,simulation-basedmethodstoperformoptimalstatees-theperformanceofSMCalgorithmsdependsheavilyontimationinnon-linearnon-Gaussianstatespacemodelsthevariousparametersofthealgorithms.Considerfor[SI.Inth

4、isapproach,theposteriorprobabilitydistri-exampletheclassofSequentialImportanceSamplingbutionsofinterestareestimatedusingacloudofran-Resampling(SISR)algorithms[7].Currentalgorithmsdomsampleswhicharecarriedovertimeusingimpor-aretypicallydesignedsoastooptimizesome“lo

5、cal”tancesamplingandresamplingtechniques.Currental-criteriasuchastheconditionalvarianceoftheimpor-gorithmsaretypicallydesignedsoastooptimizesometanceweightsintheimportancesamplingsteporthe“local1’criteriasuchastheconditionalvarianceoftheconditionalvarianceofthenum

6、berofoffspringintheimportanceweightsintheimportancesamplingstep.resamplingstep.However,theeffectoftheselocalopti-However,theeffectoftheselocaloptimizationsisnotmizationsisnotclearontheglobalperformanceoftheclearontheglobalperformanceofthealgorithm;e.g.algorithm.Fo

7、rexample,samplingwithanon-locally.samplingwithanon-locallyoptimalimportancedistri-optimalimportancedistributionatagiventimecouldbutionmightbebeneficialatfurthertimesteps.Webebeneficialatfurthertimesteps.Soevenifoptimiz-presenthereanaltemativeprincipledapproachwher

8、eing“local”criteriaissensible,onewouldpreferinap-theSMCisparametrizedanditsparametersoptimizedplicationstodesignanalgorithmoptimizinga“global”withrespec